SCIENCE JOKES
ver 6.2 jan 23, 1995
Collected by Joachim Verhagen (verhagen@fys.ruu.nl)
Includes collection by Lars Olofsson (larso@wmute.trillium.se) of april 1994
Includes math jokes collection by Michael Cook (mlc@iberia.cca.rockwell.com)
of june 1994
Includes collection by Chris Bradfield (ph2008@bris.ac.uk) of oktober 1994
Codes for subjects:
M mathematics ; P physics ; C chemistry ; B biology ; E engineering
A computer science.
Contents
=1. The mathematician, the physicist and the engineer (and other professions)
=2. Mathematics
=2.1 proofs
=2.2 statistics and statisticans
=2.3 mathematicians
=2.4 poetry
=2.5 quotes
=3. physics
=3.1 poetry
=3.2 quotes
=4. chemistry
=4.1 poetry
=5. miscellany
=5.1 poetry
=5.2 quotes
=6. anecdotes about scientists
=7. mnemonics
=7.1 mnemonics
=7.2 mathematics
=7.3 computer science
=7.4 physics
=7.5 chemistry
=7.6 biology and medicine
=7.7 miscellany
=8. pranks
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=1. THE MATHEMATICAN, THE PHYSICIST AND THE ENGINEER (AND OTHER PROFESSIONS)
MPE________________________________________________________________________
jwest@jwest.ecen.okstate.edu:
A mathmatician, a physicist, and an engineer were all given a red rubber
ball and told to find the volume. The mathmatician carefully measured
the diamaeter and evaluated a triple integral. The physicist filled a
beaker with water, put the ball in the water, and measured the total
displacement. The engineer looked up the model and serial numbers in
his red-rubber-ball table.
If it was my company: The engineer tried to look up the model and serial
numbers, couldn't find them, so told his manager that it's just not going
to work.
MP_________________________________________________________________________
A mathematician and a physicist agree to a psychological experiment.
The mathematician is put in a chair in a large empty room and a
beautiful naked woman is placed on a bed at the other end of the room.
The psychologist explains, "You are to remain in your chair. Every
five minutes, I will move your chair to a position halfway between its
current location and the woman on the bed." The mathematician looks
at the psychologist in disgust. "What? I'm not going to go through
this. You know I'll never reach the bed!" And he gets up and storms
out. The psychologist makes a note on his clipboard and ushers the
physicist in. He explains the situation, and the physicist's eyes
light up and he starts drooling. The psychologist is a bit confused.
"Don't you realize that you'll never reach her?" The physicist smiles
and replied, "Of course! But I'll get close enough for all practical
purposes!"
MP_________________________________________________________________________
Dean, to the physics department. "Why do I always have to give you
guys so much money, for laboratories and expensive equipment and
stuff. Why couldn't you be like the math department - all they need
is money for pencils, paper and waste-paper baskets. Or even better,
like the philosophy department. All they need are pencils and paper."
MPE________________________________________________________________________
An engineer, physicist, and mathematician are all challenged with a
problem: to fry an egg when there is a fire in the house. The
engineer just grabs a huge bucket of water, runs over to the fire, and
puts it out. The physicist thinks for a long while, and then measures
a precise amount of water into a container. He takes it over to the
fire, pours it on, and with the last drop the fire goes out. The
mathematician pores over pencil and paper. After a few minutes he
goes "Aha! A solution exists!" and goes back to frying the egg.
Sequel: This time they are asked simply to fry an egg (no fire). The
engineer just does it, kludging along; the physicist calculates
carefully and produces a carefully cooked egg; and the mathematician
lights a fire in the corner, and says "I have reduced it to the
previous problem."
PEA________________________________________________________________________
From: pascual@tid.es (Pascual de Juan Nuqez)
Three men, a physican, a engineer and a computer scientist, are
travelling in a car. Suddenly, the car starts to smoke and stops.
The three atonished men try to solve the problem:
- Physican says: This is obviously a classic problem of torque.
It has been overloaded the elasticity limit of
the main axis.
- Engineer says : Let's be serious! The matter is that it has been
burned the spark of the connecting rod to the dynamo
of the radiator. I can easily repair it by hammering.
- Computer scientist says : What if we get off the car, wait a minute,
and then get in and try again?
MEA________________________________________________________________________
An engineer, a mathematician, and a computer programmer are driving
down the road when the car they are in gets a flat tire. The engineer
says that they should buy a new car. The mathematician says they
should sell the old tire and buy a new one. The computer programmer
says they should drive the car around the block and see if the tire
fixes itself.
MPEA_______________________________________________________________________
Sender: karl@modi.diku.dk
david@ittpub.nl (David P. Morgan):
Several students were asked the following problem:
Prove that all odd integers higher than 2 are prime.
Well, the first student to try to do this was a math student. Hey
says "Hmmm... Well, 3 is prime, 5 is prime, 7 is prime, and by
induction, we have that all the odd integers are prime."
Of course, there are some jeers from some of his friends. The physics
student then said, "I'm not sure of the validity of your proof, but I
think I'll try to prove it by experiment." He continues, "Well,
3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an
experimental error, 11 is prime, 13 is prime... Well, it seems that
you're right."
The third student to try it was the engineering student, who
responded, "Well, actually, I'm not sure of your answer either. Let's
see... 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is
..., well if you approximate, 9 is prime, 11 is prime, 13 is prime...
Well, it does seem right."
Not to be outdone, the computer science student comes along and says
"Well, you two sort've got the right idea, but you'd end up taking too
long doing it. I've just whipped up a program to REALLY go and prove
it..." He goes over to his terminal and runs his program. Reading
the output on the screen he says, "1 is prime, 1 is prime, 1 is prime,
1 is prime...."
Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime,
segmentation fault
Software tech support operator: Well, we haven't had any reports of
composite odd numbers... do you have the latest version of ZFC?
Logician:
Hypothesis: All odd numbers are prime
Proof:
1) If a proof exists, then the hypothesis must be true
2) The proof exists; you're reading it now.
From 1 and 2 follows that all odd numbers are prime
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman)
Confused undergraduate: Yes, it's true. Proof: Let p be any prime
number larger than 2. Then p is not divisible by 2, so p is odd. QED
From: chris@labtam.labtam.oz.au (Chris Taylor)
Wouldn't a modern physicist employ something like renormalization?
3 is prime, 5 is prime, 7 is prime, 9 is ...
9/3 is prime
11 is prime, 13 is prime, 15 is ...
15/3 is prime
17 is prime, 19 is prime, 21 is ...
21/3 is prime
Quantum Physics: All numbers are equally prime and non-prime until observed.
From: barry@numetrix.com (Barry Fruitman)
English Major:
1 is prime, 2 is prime, 3 is prime, 4 is prime...
Any fool could prove that the above is wrong...
After all, no English major can count that high! ;-)
P.S. And I should know...I've done^H^H^H^H spent time in the English army!
biologist or accountant or doctor or ...
Duh, what's a prime ?
MBA________________________________________________________________________
A biologist, a statistician, a mathematician and a computer scientist are
on a photo-safari in Africa. They drive out into the savannah in their
jeep, stop and scour the horizon with their binoculars.
The biologist: "Look! There's a herd of zebras! And there, in the middle:
a white zebra! It's fantastic! There are white zebras! We'll be famous!"
The statistician:
"It's not significant. We only know there's one white zebra"
The mathematician:
"Actually, we know there exists a zebra which is white on one side"
The computer scientist:
"Oh no! A special case!"
MPA________________________________________________________________________
A philosopher, a physicist, a mathematician and a computer scientist were
travelling through Scotland when they saw a black sheep through the
window of the train.
"Aha," says the philosopher, "I see that Scottish sheep are black."
"Hmm," says the physicist, "You mean that some Scottish sheep are
black."
"No," says the mathematician, "All we know is that there is at least
one sheep in Scotland, and that at least one side of that one sheep is
black!"
"Oh, no!" shouts the computer scientist, "A special case!"
Sherlock Holmes and Dr. Watson were travelling on the same train
when they passed the same field full of sheep.
"Look at that solitary black sheep among all those white ones" said
Watson to Holmes.
"Yes Watson, the ratio of black sheep to white in that field is
one black to three hundred and seventeen white" replied Holmes.
"But how can you be so precise" said Watson, flabbergasted.
"Elementary, my dear Watson" replied Holmes, "I counted all of the
legs and divided by four!"
MEA________________________________________________________________________
The problem with engineers is that they tend to cheat in order to get
results.
The problem with mathematicians is that they tend to work on toy
problems in order to get results.
The problem with program verifiers is that they tend to cheat at toy
problems in order to get results.
ME_________________________________________________________________________
From: levd@alien (Lev Desmarais)
The difference between an Engineer and a Mathematician :
The Engineer walks in her office and finds her trash can on fire. She
gets the fire extinguisher and puts out the fire.
The Mathematician walks in his office and finds his trash can on fire.
He gets the fire extinguisher and puts out the fire.
The following day :
The Engineer walks in her office and finds the trash can on fire on
top of her desk. She gets the fire extinguisher and put out the fire.
The Mathematician walks in his office and finds the trash can on fire
on top of his desk. He takes the trash can and puts it on the floor.
He has reduced the problem to a previously solved state. Too solve it
again would be redundant.
MP_________________________________________________________________________
A physicist and a mathematician setting in a faculty lounge.
Suddenly, the coffee machine catches on fire. The physicist grabs a
bucket and leaps towards the sink, fills the bucket with water and
puts out the fire. The second day, the same two sit in the same
lounge. Again, the coffee machine catches on fire. This time, the
mathematician stands up, gets a bucket, hands the bucket to the
physicist, thus reducing the problem to a previously solved one.
MPE________________________________________________________________________
An engineer, a mathematician, and a physicist are staying in three
adjoining cabins at a decrepit old motel.
First the engineer's coffee maker catches fire on the bathroom vanity.
He smells the smoke, wakes up, unplugs it, throws it out the window,
and goes back to sleep.
Later that night the physicist smells smoke too. He wakes up and sees
that a cigarette butt has set the trash can on fire. He says to
himself, "Hmm. How does one put out a fire? One can reduce the
temperature of the fuel below the flash point, isolate the burning
material from oxygen, or both. This could be accomplished by applying
water." So he picks up the trash can, puts it in the shower stall,
turns on the water, and, when the fire is out, goes back to sleep.
The mathematician, of course, has been watching all this out the
window. So later, when he finds that his pipe ashes have set the
bedsheet on fire, he is not in the least taken aback. He immediately
sees that the problem reduces to one that has already been solved and
goes back to sleep.
MPE________________________________________________________________________
From: dhein@onramp.net
An Engineer, a Physicist, and a Mathematician all go the same
Conference. University budgets being what they are, they all stay in
the same cheap hotel. Each room has the same floor plan, has the same
cheap TV, the same cheap bed, and a small bathroom. Instead of
a sprinkler system, the hotel has opted for Fire Buckets.
The Engineer, Physicist, and Mathematician are all asleep in bed. At
about 2AM, the Engineer wakes up because he smells smoke. He looks in
the corner of the room and sees that the TV set is on fire! He dashes
into the bathroom, fills the Fire Bucket to overflowing with water, and
drenches the TV set. The fire goes out, and the Engineer goes back to
sleep.
A little while later, the Physicist wakes because he smells smoke. He
looks in the corner and sees that the TV set is on fire. He grabs a
handy envelope, estimates the BTU output of the fire, scribbles a quick
calculation, then dashes into the bathroom and fills the Fire Bucket
with just enough water to douse the flames. He puts the fire out and
goes back to sleep.
In a little while, the Mathematician wakes up to the smell of smoke.
He looks in the corner and sees the TV on fire. He looks into the
bathroom and sees the Fire Bucket. Having determined that a solution
exists, he goes back to sleep.
MPE________________________________________________________________________
A physicist, an engineer and a mathematician were all in a hotel
sleeping when a fire broke out in their respective rooms.
The physicist woke up, saw the fire, ran over to his desk, pulled
out his CRC, and began working out all sorts of fluid dynamics
equations. After a couple minutes, he threw down his pencil, got
a graduated cylinder out of his suitcase, and measured out a
precise amount of water. He threw it on the fire, extinguishing
it, with not a drop wasted, and went back to sleep.
The engineer woke up, saw the fire, ran into the bathroom, turned
on the faucets full-blast, flooding out the entire apartment,
which put out the fire, and went back to sleep.
The mathematician woke up, saw the fire, ran over to his desk,
began working through theorems, lemmas, hypotheses , you -name-it,
and after a few minutes, put down his pencil triumphantly and
exclaimed, "I have *proven* that I *can* put the fire out!"
He then went back to sleep.
MP_________________________________________________________________________
A mathematician and a physicist were asked the following question:
Suppose you walked by a burning house and saw a hydrant and
a hose not connected to the hydrant. What would you do?
P: I would attach the hose to the hydrant, turn on the water, and put out
the fire.
M: I would attach the hose to the hydrant, turn on the water, and put out
the fire.
Then they were asked this question:
Suppose you walked by a house and saw a hose connected to
a hydrant. What would you do?
P: I would keep walking, as there is no problem to solve.
M: I would disconnect the hose from the hydrant and set the house on fire,
reducing the problem to a previously solved form.
E__________________________________________________________________________
The graduate with a Science degree asks, "Why does it work?"
The graduate with an Engineering degree asks, "How does it work?"
The graduate with an Accounting degree asks, "How much will it cost?"
The graduate with a Liberal Arts degree asks, "Do you want mustard with
that?"
MPCE_______________________________________________________________________
A lecturer tells some students to learn the phone-book by heart.
The mathematicians are baffled: `By heart? You kidding?'
The physics-students ask: `Why?'
The engineers sigh: `Do we have to?'
The chemistry-students ask: `Till next Monday?'
The accounting-students (scribbling): `Till tomorrow?'
The laws-students answer: `We already have.'
The medicine-students ask: `Should we start on the Yellow Pages?'
MPE________________________________________________________________________
The engineer thinks of his equations as an approximation to reality.
The physicist thinks reality is an approximation to his equations.
The mathematician doesn't care.
MPB________________________________________________________________________
Three men with degrees in mathmatics, physics and biology are locked
up in dark rooms for research reasons.
A week later the researchers open the a door, the biologist steps out
and reports: `Well, I sat around until I started to get bored, then
I searched the room and found a tin which I smashed on the floor.
There was food in it which I ate when I got hungry. That's it.'
Then they free the man with the degree in physics and he says:
`I walked along the walls to get an image of the room's geometry, then
I searched it. There was a metal cylinder at five feet into the room
and two feet left of the door. It felt like a tin and I threw it at
the left wall at the right angle and velocity for it to crack open.'
Finally, the researchers open the third door and hear a faint voice
out of the darkness: `Let C be an open can.'
M__________________________________________________________________________
A doctor, a lawyer and a mathematician were discussing the relative
merits of having a wife or a mistress.
The lawyer says: "For sure a mistress is better. If you have a wife
and want a divorce, it causes all sorts of legal problems.
The doctor says: "It's better to have a wife because the sense of
security lowers your stress and is good for your health.
The mathematician says: " You're both wrong. It's best to have both so
that when the wife thinks you're with the mistress and the mistress
thinks you're with your wife --- you can do some mathematics.
MPB________________________________________________________________________
A Mathematician, a Biologist and a Physicist are sitting in a street cafe
watching people going in and coming out of the house on the other side
of the street.
First they see two people going into the house. Time passes.
After a while they notice three persons coming out of the house.
The Physicist: "The measurement wasn't accurate.".
The Biologists conclusion: "They have reproduced".
The Mathematician: "If now exactly 1 person enters the house then it will be
empty again."
ME_________________________________________________________________________
There were two men trying to decide what to do for a living. They
went to see a counselor, and he decided that they had good problem
solving skills.
He tried a test to narrow the area of specialty. He put each man in a
room with a stove, a table, and a pot of water on the table. He said
"Boil the water". Both men moved the pot from the table to the stove
and turned on the burner to boil the water. Next, he put them into a
room with a stove, a table, and a pot of water on the floor. Again,
he said "Boil the water". The first man put the pot on the stove and
turned on the burner. The counselor told him to be an Engineer,
because he could solve each problem individually. The second man
moved the pot from the floor to the table, and then moved the pot from
the table to the stove and turned on the burner. The counselor told
him to be a mathematician because he reduced the problem to a
previously solved problem.
E__________________________________________________________________________
Three engineering students were gathered together discussing the possible
designers of the human body.
One said, ``It was a mechanical engineer. Just look at all the joints.''
Another said, ``No, it was an electrical engineer. The nervous system has
many thousands of electrical connections.''
The last said, ``Actually it was a civil engineer. Who else would run a
toxic waste pipeline through a recreational area?''
MPE________________________________________________________________________
An engineer, a physicist, and a mathematician are shown a pasture
with a herd of sheep, and told to put them inside the smallest
possible amount of fence. The engineer is first. He herds the sheep
into a circle and then puts the fence around them, declaring, "A
circle will use the least fence for a given area, so this is the
best solution." The physicist is next. She creates a circular fence of
infinite radius around the sheep, and then draws the fence tight around
the herd, declaring, "This will give the smallest circular fence around
the herd." The mathematician is last. After giving the problem a little
thought, he puts a small fence around himself and then declares, "I
define myself to be on the outside!"
MPE________________________________________________________________________
One day a farmer called up an engineer, a physicist, and a mathematician
and asked them to fence of the largest possible area with the least
amount of fence. The engineer made the fence in a circle and
proclaimed that he had the most efficient design. The physicist made
a long, straight line and proclaimed 'We can assume the length is
infinite...' and pointed out that fencing off half of the Earth was
certainly a more efficient way to do it. The Mathematician just
laughed at them. He built a tiny fence around himself and said 'I
declare myself to be on the outside.'
EC_________________________________________________________________________
Four men were sitting one day discussing how smart their dog's were.
The first man was an Engineer, who said his dog could do math. His dog
was named T-Square, and he told him to get some paper and draw a square,
a circle, and a triangle, which the dog did with no sweat.
The Accountant said that his dog was better. His dog, Slide Rule, was
told to fetch a dozen cookies, bring them back, and divide them into
piles of 3, which Slide Rule did with no problem.
The Chemist said his dog was smarter, his dog named Measure, was told to
get a quart of milk, and pour 7 ounces into a 10 ounce glass. The dog
did this with no trouble at all, and all three men agreed that their
dog's were equally smart.
Then they turned to the Union Member and asked, what can your dog do?
The Union Member called his dog, who was named Coffee Break, and said,
"Show the fellows what you can do".
Coffee Break went over and ate the cookies, drank the milk, shit on the
paper, fucked the other dogs, and claimed he injured his back while
doing so, filed a grievence report for unsafe working conditions, put in
for Workmens Compensation, and left for home on sick leave.
MP_________________________________________________________________________
A mathematician and a physicist are given the task of describing a room.
They both go in, and spend hours meticulously writing down every detail,
each turning in nearly a ream of paper. The next day, the room is changed,
and they are again given the task. The physicist spends the better part
of the day, but the mathematician, amazingly enough, leaves within a
minute. he hands in a single sheet of paper with the following
description:
Put picture back on wall to return to previously solved state.
ME_________________________________________________________________________
To tell a difference between a mathematician and an engineer, perform
this experiment. Put an empty kettle in the middle of the kitchen
floor and tell your subjects to boil some water.
The engineer will fill the kettle with water, put it on the stove, and
turn the flame on. The mathematician will do the same thing.
Next, put the kettle already filled with water on the stove, and ask
the subjects to boil the water. The engineer will turn the flame on.
The mathematician will empty the kettle and put it in the middle of
the kitchen floor... thereby reducing the problem to one that has
already been solved!
MPE________________________________________________________________________
So a mathematician, an engineer, and a physicist are out hunting
together. They spy a deer(*) in the woods.
The physicist calculates the velocity of the deer and the effect of
gravity on the bullet, aims his rifle and fires. Alas, he misses; the
bullet passes three feet behind the deer. The deer bolts some yards,
but comes to a halt, still within sight of the trio.
"Shame you missed," comments the engineer, "but of course with an
ordinary gun, one would expect that." He then levels his special
deer-hunting gun, which he rigged together from an ordinary rifle, a
sextant, a compass, a barometer, and a bunch of flashing lights which
don't do anything but impress onlookers, and fires. Alas, his bullet
passes three feet in front of the deer, who by this time wises up and
vanishes for good.
"Well," says the physicist, "your contraption didn't get it either."
"What do you mean?" pipes up the mathematician. "Between the two of
you, that was a perfect shot!"
(*) How they knew it was a deer:
The physicist observed that it behaved in a deer-like manner, so it
must be a deer.
The mathematician asked the physicist what it was, thereby reducing it
to a previously solved problem.
The engineer was in the woods to hunt deer, therefore it was a deer.
MPE________________________________________________________________________
A Mathematician (M) and an Engineer (E) attend a lecture by a
Physicist. The topic concerns Kulza-Klein theories involving physical
processes that occur in spaces with dimensions of 9, 12 and even
higher. The M is sitting, clearly enjoying the lecture, while the E
is frowning and looking generally confused and puzzled. By the end
the E has a terrible headache. At the end, the M comments about the
wonderful lecture. The E says "How do you understand this stuff?"
M: "I just visualize the process."
E: "How can you POSSIBLY visualize something that occurs in
9-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N go to 9."
MPE________________________________________________________________________
What is "pi"?
Mathematician: Pi is the number expressing the relationship between the
circumference of a circle and its diameter.
Physicist: Pi is 3.1415927 plus or minus 0.000000005
Engineer: Pi is about 3.
MPE________________________________________________________________________
When considering the behaviour of a howitzer:
A mathematician will be able to calculate where the shell will land.
A physicist will be able to explain how the shell gets there.
An engineer will stand there and try to catch it.
MPE________________________________________________________________________
There was a mad scientist ( a mad ...social... scientist ) who
kidnapped three colleagues, an engineer, a physicist, and a
mathematician, and locked each of them in seperate cells with plenty
of canned food and water but no can opener.
A month later, returning, the mad scientist went to the engineer's
cell and found it long empty. The engineer had constructed a can
opener from pocket trash, used aluminum shavings and dried sugar to
make an explosive, and escaped.
The physicist had worked out the angle necessary to knock the lids off
the tin cans by throwing them against the wall. She was developing a
good pitching arm and a new quantum theory.
The mathematician had stacked the unopened cans into a surprising
solution to the kissing problem; his desiccated corpse was propped
calmly against a wall, and this was inscribed on the floor in blood:
Theorem: If I can't open these cans, I'll die.
Proof: assume the opposite...
MPCB_______________________________________________________________________
The USDA once wanted to make cows produce milk faster, to improve the
dairy industry.
So, they decided to consult the foremost biologists and recombinant
DNA technicians to build them a better cow. They assembled this team
of great scientists, and gave them unlimited funding. They requested
rare chemicals, weird bacteria, tons of quarantine equipment, there
was a horrible typhus epidemic they started by accident, and, 2 years
later, they came back with the "new, improved cow." It had a milk
production improvement of 2% over the original.
They then tried with the greatest Nobel Prize winning chemists around.
They worked for six months, and, after requisitioning tons of chemical
equipment, and poisoning half the small town in Colorado where they
were working with a toxic cloud from one of their experiments, they
got a 5% improvement in milk output.
The physicists tried for a year, and, after ten thousand cows were
subjected to radiation therapy, they got a 1% improvement in output.
Finally, in desperation, they turned to the mathematicians. The
foremost mathematician of his time offered to help them with the
problem. Upon hearing the problem, he told the delegation that they
could come back in the morning and he would have solved the problem.
In the morning, they came back, and he handed them a piece of paper
with the computations for the new, 300% improved milk cow.
The plans began:
"A Proof of the Attainability of Increased Milk Output from Bovines:
Consider a spherical cow......"
MPCE_______________________________________________________________________
An assemblage of the most gifted minds in the world were all posed the
following question:
"What is 2 * 2 ?"
The chemist says immediately circa 10 to the power 1.
The engineer whips out his slide rule (so it's old) and shuffles it
back and forth, and finally announces "3.99".
The physicist consults his technical references, sets up the problem
on his computer, and announces "it lies between 3.98 and 4.02".
The mathematician cogitates for a while, oblivious to the rest of the
world, then announces: "I don't what the answer is, but I can tell
you, an answer exists!".
Philosopher: "But what do you _mean_ by 2 * 2 ?"
Logician: "Please define 2 * 2 more precisely."
Accountant: Closes all the doors and windows, looks around carefully,
then asks "What do you _want_ the answer to be?"
Computer Hacker: Breaks into the NSA super-computer and gives the answer.
MP_________________________________________________________________________
From: MARTIN.VIETOR@HEIDEBOX.HEIDE.DE (Translation to blame on Joachim)
A mathematician, a physicist and a doctor were posed the questin 2*2.
The physicist takes a notebook and starts scribbling. After 3 days of the
most complex calculations he finds with use of the Earth radius, the
gravitation constant : "Somewhere between pi and 2 times the square root
of 3."
The mathematican comes back after a week with dark rings under his eyes
and proclaims: "Colleges, their is a solution."
The doctor says simple :"4"
The others answer: "Oh well you memorized it."
MPA________________________________________________________________________
Philosopher: "Resolution of the continuum hypothesis will have
profound implications to all of science."
Physicist: "Not quite. Physics is well on its way without those
mythical `foundations'. Just give us serviceable mathematics."
Computer Scientist:
"Who cares? Everything in this Universe seems to be finite
anyway. Besides, I'm too busy debugging my Pascal programs."
Mathematician:
"Forget all that! Just make your formulae as aesthetically
pleasing as possible!"
PE_________________________________________________________________________
From: "F. Ted Tschang"
An economist, an engineer, and a physicist are marooned on a deserted
island. One day they find a can of food washed up on the beach and
contrive to open it. The engineer said: "let's hammer the can open
between these rocks". The physicist said: "that's pretty crude. We can
just use the force of gravity by dropping a rock on the can from that
tall tree over there". The economist is somewhat disgusted at these
deliberations, and says: "I've got a much more elegant solution. All we
have to do is assume a can-opener."
E__________________________________________________________________________
In some foreign country a priest, a lawyer and an engineer are
about to be guillotined. The priest puts his head on the block,
they pull the rope and nothing happens -- he declares that he's
been saved by divine intervention -- so he's let go. The lawyer
is put on the block, and again the rope doesn't release the
blade, he claims he can't be executed twice for the same crime
and he is set free too. They
grab the engineer and shove his head into the
guillotine, he looks up at the release mechanism and says, "Wait
a minute, I see your problem......"
MP_________________________________________________________________________
Einstein dies and goes to heaven only to be informed that his room is
not yet ready. "I hope you will not mind waiting in a dormitory. We
are very sorry, but it's the best we can do and you will have to share
the room with others." he is told by the doorman (say his name is
Pete). Einstein says that this is no problem at all and that there is
no need to make such a great fuss. So Pete leads him to the dorm.
They enter and Albert is introduced to all of the present
inhabitants. "See, Here is your first room mate. He has an IQ of
180!"
"Why that's wonderful!" Says Albert. "We can discuss mathematics!"
"And here is your second room mate. His IQ is 150!"
"Why that's wonderful!" Says Albert. "We can discuss physics!"
"And here is your third room mate. His IQ is 100!"
"That Wonderful! We can discuss the latest plays at the theater!"
Just then another man moves out to capture Albert's hand and shake it.
"I'm your last room mate and I'm sorry, but my IQ is only 80."
Albert smiles back at him and says, "So, where to you think interest
rates are headed?"
MPE________________________________________________________________________
An engineer, a mathematician, and a physicist went to the races one
Saturday and laid their money down. Commiserating in the bar after
the race, the engineer says, "I don't understand why I lost all my
money. I measured all the horses and calculated their strength and
mechanical advantage and figured out how fast they could run..."
The physicist interrupted him: "...but you didn't take individual
variations into account. I did a statistical analysis of their
previous performances and bet on the horses with the highest
probability of winning..."
"...so if you're so hot why are you broke?" asked the engineer. But
before the argument can grow, the mathematician takes out his pipe and
they get a glimpse of his well-fattened wallet. Obviously here was a
man who knows something about horses. They both demanded to know his
secret.
"Well," he says, between puffs on the pipe, "first I assumed all the
horses were identical and spherical..."
MPE________________________________________________________________________
A group of scientists were doing an investigation into problem-solving
techniques, and constructed an experiment involving a physicist, an
engineer, and a mathematician.
The experimental apparatus consisted of a water spigot and two identical
pails, one of which was fastened to the ground ten feet from the spigot.
Each of the subjects was given the second pail, empty, and told to fill the
pail on the ground.
The physicist was the first subject: he carried his pail to the spigot,
filled it there, carried it full of water to the pail on the ground, and
poured the water into it. Standing back, he declared, "There: I have
solved the problem."
The engineer and the mathematician each approached the problem similarly.
Upon finishing, the engineer noted that the solution was exact, since the
volumes of the pails were equal. The mathematician merely noted that he
had proven that a solution exists.
Now, the experimenters altered the parameters of the task a bit: the pail
on the ground was still empty, but the subjects were presented with a pail
that was already half-filled with water.
The physicist immediately carried his pail over to the one on the ground,
emptied the water into it, went back to the spigot, *filled* the pail, and
finally emptied the entire contents into the pail on the ground,
overflowing it and spilling some of the water. Upon finishing, he
commented that the problem should have been better stated.
The engineer, in turn, thought for some time before going into action. He
then took his half-filled pail to the spigot, filled it to the brim, and
filled the pail on the ground from it. Again he noted that the problem had
an exact solution, which of course he had found.
The mathematician thought for a long time before stirring. At last he
stood up, emptied his pail onto the ground, and declared, "The problem has
been reduced to one already solved."
A__________________________________________________________________________
A doctor, an architect, and a computer scientist were arguing
about whose profession was the oldest. In the course of their
arguments, they got all the way back to the Garden of Eden, whereupon
the doctor said, "The medical profession is clearly the oldest, because
Eve was made from Adam's rib, as the story goes, and that was a simply
incredible surgical feat."
The architect did not agree. He said, "But if you look at the
Garden itself, in the beginning there was chaos and void, and out of
that, the Garden and the world were created. So God must have been an
architect."
The computer scientist, who had listened to all of this said,
"Yes, but where do you think the chaos came from?"
PCE________________________________________________________________________
From: chemistrwb@aol.com (ChemistRWB)
A chemist, a physicist and an Engineer went on a camping trip, accompanied
by a guide. The were brought to a cabin in the deep Canadian wilderness.
Inside the cabin was a wood-burning stove, but it was set up on bricks
about 60 cm above the floor of the cabin. The three scientists speculated
about the function of the high placement of the stove. The chemist said,
"Obviously, the guide has anticipated the convection currents of the heat
an placed the stove in a raised position to maximize the heat flow in the
semi-adiabatic system." The Physicist believed, "No, it's far simpler
than that, the guide placed the stove higher so movement from the
countertops to the stove would be minimized and energy conserved." The
engineer believed he had the true answer, "Obviously, you fellows don't do
much camping. The stove is place higher so we can bring in wood and put
it under the stove to dry." The guide soon returned and all three
scientists were eager to find out who was right. The guide replied,
"Well, we was bringin' the dang thing up the river and part of the chimney
pipe fell off the boat, so we had to put it up for the pipe to reach the
ceiling."
PS: If you know all the words in this essay, your English is better than
99% of native Americans.
MPE________________________________________________________________________
From: grayd@is.dal.ca (James D. Gray)
An Engineering Student, a Physics Student, and a Mathematics student were
each given $150 dollars and were told to use that money to find out exactly
how tall a particular hotel was.
All three ran off, extremely keen on how to do this. The Physics
student went out, purchased some stopwatches, a number of ball bearings,
a calculator, and some friends. He had them all time the drop of ball
bearings from the roof, and he then figured out the height from the time
it took for the bearings to accelerate from rest until they impacted with
the sidewalk.
The Math student waited until the sun was going down, then she
took out her protractor, plumb line, measuring tape,and scratch pad,
measured the length of the shadow, found the angle the buildings roof
made from the ground, and used trignometry to figure out the height of
the building.
These two students bumped into the Engineering student the next
day, who was nursing a really bad hangover. When asked what he did to
find the height of the building he replied:
"Well, I walked up to the bell hop, gave him 10 bucks, asked him
how tall the hotel was, and hit the bar inside for happy hour!"
MPE________________________________________________________________________
An engineer, a physicist and a mathematician find themselves in an
anecdote, indeed an anecdote quite similar to many that you have no
doubt already heard. After some observations and rough calculations
the engineer realizes the situation and starts laughing. A few
minutes later the physicist understands too and chuckles to himself
happily as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed
right away that he was the subject of an anecdote, and deduced quite
rapidly the presence of VariEventuali from similar anecdotes, but considers
this anecdote to be too trivial a corollary to be significant, let
alone funny.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=2. MATHEMATICS
M__________________________________________________________________________
From: guest@se.alcbel.be:
rafy@cairo.anu.edu.au (Rafy Marootians):
Logic is a systematic method for getting the wrong conclusion...
with confidence.
Surely _statistics_ is a systematic method for getting the wrong conclusion...
with 95% confidence.
From: phk@data.fls.dk (Poul-Henning Kamp/P-HK)
Mathematics is the systematic misuse of a nomenclature developed for that
specific purpose.
M__________________________________________________________________________
A topologist is a man who doesn't know the difference between a coffee
up and a doughnut.
M__________________________________________________________________________
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman)
Most prime numbers are even.
Proof: pick up any math text and look
for a prime number. The first one you
find will probably be even.
M__________________________________________________________________________
Once upon a time, when I was training to be a mathematician, a group of
us bright young students taking number theory discovered the names of
the smaller prime numbers.
2: The Odd Prime --
It's the only even prime, therefore is odd. QED.
3: The True Prime --
Lewis Carroll: "If I tell you three times, it's true."
31: The Arbitrary Prime --
Determined by unanimous unvote. We needed an arbitrary prime
in case the prof asked for one, and so had an election. 91
received the most votes (well, it *looks* prime) and 3+4i the
next most. However, 31 was the only candidate to receive none
at all.
Since the composite numbers are formed from primes, their qualities are
derived from those primes. So, for instance, the number 6 is "odd but
true", while the powers of 2 are all extremely odd numbers.
M__________________________________________________________________________
From: Tpotter@voyager.cris.com (Tom_Potter)
Tom Potter: Life is complex. It has real and imaginary components.
M__________________________________________________________________________
From: Erland.Gadde@sm.luth.se (Erland Gadde)
Trigonometry for farmers: swine and cowswine.
M__________________________________________________________________________
From: mstueben@pen.k12.va.us (Michael A. Stueben)
I liked the PI-ous one best.
M__________________________________________________________________________
Q: What does an analytic number theoriest say when he is drowning?
A: Log-log, log-log, log-log, . . .
M__________________________________________________________________________
From: Alan Craig
Mathematicians have announced the existence of a new whole number which lies
between 27 and 28. "We don't know why it's there or what it does," says
Cambridge mathematician, Dr. Hilliard Haliard, "we only know that it doesn't
behave properly when put into equations, and that it is divisible by six,
though only once."
M__________________________________________________________________________
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman)
"The number you have dialed is imaginary.
Please rotate your phone 90 degrees and try again."
M__________________________________________________________________________
From: david_gonda@qm.yale.edu
A student was doing miserably on his oral final exam in General Toplogy
(yes, this guy _really_ did give oral finals in topology). Exasperated by
the student's abysmal performance up to that point, the professor asked the
student "So, what _do_ you know about topology?" The student replied, "I
know the definition of a topologist." The professor asked him to state the
definition, expecting to get the old saw about someone who can't tell the
difference between a coffee cup and a doughnut. Instead, the student
replied: "A topologist is someone who can't tell the difference between his
ass and a hole in the ground, but who can tell the difference between his
ass and _two_ holes in the ground."
The student passed.
M__________________________________________________________________________
Definitions of Terms Commonly Used in Higher Math
The following is a guide to the weary student of mathematics who
is often confronted with terms which are commonly used but rarely
defined. In the search for proper definitions for these terms we
found no authoritative, nor even recognized, source. Thus, we
followed the advice of mathematicians handed down from time
immortal: "Wing It."
CLEARLY: I don't want to write down all the "in-
between" steps.
TRIVIAL: If I have to show you how to do this, you're
in the wrong class.
OBVIOUSLY: I hope you weren't sleeping when we discussed
this earlier, because I refuse to repeat it.
RECALL: I shouldn't have to tell you this, but for
those of you who erase your memory tapes
after every test...
WLOG (Without Loss Of Generality): I'm not about to do all the
possible cases, so I'll do one and let you
figure out the rest.
IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
be able to prove this without me holding your
hand.
CHECK or CHECK FOR YOURSELF: This is the boring part of the
proof, so you can do it on your own time.
SKETCH OF A PROOF: I couldn't verify all the details, so I'll
break it down into the parts I couldn't
prove.
HINT: The hardest of several possible ways to do a
proof.
BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
arguments, two long inductions, "and a
partridge in a pair tree."
SOFT PROOF: One third less filling (of the page) than
your regular proof, but it requires two extra
years of course work just to understand the
terms.
ELEGANT PROOF: Requires no previous knowledge of the subject
matter and is less than ten lines long.
SIMILARLY: At least one line of the proof of this case is
the same as before.
CANONICAL FORM: 4 out of 5 mathematicians surveyed
recommended this as the final form for their
students who choose to finish.
TFAE (The Following Are Equivalent): If I say this it means that,
and if I say that it means the other thing,
and if I say the other thing...
BY A PREVIOUS THEOREM: I don't remember how it goes (come to
think of it I'm not really sure we did this
at all), but if I stated it right (or at
all), then the rest of this follows.
TWO LINE PROOF: I'll leave out everything but the conclusion,
you can't question 'em if you can't see 'em.
BRIEFLY: I'm running out of time, so I'll just write
and talk faster.
LET'S TALK THROUGH IT: I don't want to write it on the board lest
I make a mistake.
PROCEED FORMALLY: Manipulate symbols by the rules without any
hint of their true meaning (popular in pure
math courses).
QUANTIFY: I can't find anything wrong with your proof
except that it won't work if x is a moon of
Jupiter (Popular in applied math courses).
PROOF OMITTED: Trust me, It's true.
M__________________________________________________________________________
From: mstueben@pen.k12.va.us (Michael A. Stueben)
WHAT'S OUT AND WHAT'S IN
FOR
MATHEMATICAL TERMS
by
Michael Stueben (November 7, 1994)
---------------------------------------------------------
Today it is considered an egregious faux pas to speak
or write in the crude antedated terms of our grandfathers.
To assist the isolated student and the less sophisticated
teacher, I have prepared the following list of currently
fashionable mathematical terms in academia. I pass this
list on to the general public as a matter of charity and
in the hope that it will lead to more refined elucidation
from young scholars.
OUT IN
thinking: hypothesizing.
proof by contradiction or indirect proof: reductio ad absurdum.
mistake: non sequitur.
starting place: handle.
with corresponding changes: mutatis mutandis.
counterexample: pathological exception.
consequently: ipso facto.
swallowing results: digesting proofs.
therefore: ergo.
has an easy-to-understand, but hard-to-find solution: obvious.
has two easy-to-understand, but hard-to-find solutions: trivial.
truth: tautology.
empty: vacuous.
drill problems: plug-and-chug work.
criteria: rubric.
example: substantive instantiation.
similar structure: homomorphic.
very similar structure: isomorphic.
same area: isometric.
arithmetic: number theory.
count: enumerate.
one: unity.
generally/specifically: globally/locally.
constant: invariant.
bonus result: corollary.
distance: metric measure.
several: a plurality.
function/argument: operator/operand.
separation/joining: bifurcation/confluence.
fourth power or quartic: biquadratic.
random: stochastic.
unique condition: a singularity.
uniqueness: unicity.
tends to zero: vanishes.
tip-top point: apex.
half-closed: half-open.
concave: non-convex.
rectangular prisms: parallelepipeds.
perpendicular (adj.): orthogonal.
perpendicular (n.): normal.
Euclid: Descartes.
Fermat: Wiles.
path: trajectory.
shift: rectilinear translation.
similar: homologous.
very similar: congruent.
whopper-jawed: skew or oblique.
change direction: perturb.
join: concatenate.
approximate to two or more places: accurate.
high school geometry or plane geometry: geometry of the Euclidean plane
under the Pythagorean metric.
clever scheme: algorithm.
initialize to zero: zeroize.
* : splat.
{ : squiggle.
decimal: denary.
alphabetical order: lexical order.
a divide-and-conquer method: an algorithm of logarithmic order.
student ID numbers: witty passwords.
that bitch secretary in the math dept: the witch of Agnesi
numerology and number sophistry: descriptive statistics
Special thanks to Peter Braxton who got me started
writing this stuff and who contributed five of
the items above.
M__________________________________________________________________________
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
& rja093@nwu.edu (Rajan Jain)
mathematician's PICK UP LINE
Hey baby, How would you like to join me in some math? We'll add you and me,
subtract our clothes, divide your legs, and multiply!
Of course, we'll be entirely discrete.
M__________________________________________________________________________
From: hammond@cs.utk.edu (James Michael Hammond)
When Mathematicians Go Bad
"Psst, c'mere," said the shifty-eyed man wearing a long black
trenchcoat, as he beckoned me off the rainy street into a damp dark
alley. I followed.
"What are you selling?" I asked.
"Geometrical algebra drugs."
"Huh!?"
"Geometry drugs. Ya got your uppers, your downers, your sidewaysers, your
inside-outers..."
"Stop right there," I interrupted. "I've never heard of inside-
outers."
"Oh, man, you'll love 'em. Makes you feel like M.C. ever-lovin'
Escher on a particularly weird day."
"Go on..."
"OK, your inside-outers, your arbitrary bilinear mappers, and here,
heh, here are the best ones," he said, pulling out a large clear
bottle of orange pills.
"What are those, then?" I asked.
"Givens transformers. They'll rotate you about more planes than you
even knew existed."
"Sounds gross. What about those bilinear mappers?"
"There's a whole variety of them. Here's one you'll love -- they call
it 'One Over Z' on the street. Take one of these little bad boys and
you'll be on speaking terms with the Point at Infinity."
M__________________________________________________________________________
From: v090nlb4@ubvms.cc.buffalo.edu (Mark J. VanDerwater)
halloween math
Q: Wadaya get when you take the circumference of your jack-o-lantern and
divide it by its diameter?
A: Pumpkin Pi
M__________________________________________________________________________
UR 2 Good
2 Me
2 Be
4 Got
==
10 "You are too good to me to be forgotten"
M__________________________________________________________________________
A lazy dog is a slow pup.
A slope up is an inclined plane.
An ink-lined plane is a sheet of writing-paper.
Therefore lazy dog is a sheet of writing-paper.
M__________________________________________________________________________
Complete the next two terms of this sequence:
O T T F F S S E .. ..
(A. N T - Nine Ten)
Likewise here:
3 3 5 4 4 3 5 5
(A. 4 3 -number of letters in the words "nine" and "ten").
M__________________________________________________________________________
The four branches of arithmetic - ambition, distraction, uglification and
derision. (Lewis Caroll: "Alice in Wonderland")
ME_________________________________________________________________________
The first law of Engineering Mathematics: All infinite series converge,
and moreover converge to the first term.
M__________________________________________________________________________
Numb, adj., devoid of sensation...
Number, comparative of numb.
[Webster's Third New international Dictionary]
M__________________________________________________________________________
Patageometry, n.:
The study of those mathematical properties that are invariant
under brain transplants.
M__________________________________________________________________________
kcarver@fox.nstn.ns.ca (Kevin Carver) writes:
I know most of you people who are "into" math have heard the pun (over and
over and over ...) about knowing the difference between your "asymptote and
a hole in the graph" but here's one you may not have heard. IT'S A TRUE
STORY!
A student at our high school a few years back, having had his fill with
drawing graph after graph in senior high math class, told his teacher:
Mrs. ___, I'll do algebra, I'll do trig, and I'll even do statistics, but
graphing is where I draw the line!
M__________________________________________________________________________
This one can better be told in a pub. First three points on the table:
a
b
c
On a lies a beermat and on c stands a glass. The mathematican has
to move the c to a. He takes the glas and puts it on the beermat.
Now the glas is put on point b and the mathematican has to move it
to a. The mathematican takes the glas and puts it on c - the problem
has been reduced to one already solved.
M__________________________________________________________________________
A bunch of Polish scientists decided to flee their repressive
government by hijacking an airliner and forcing the pilot to fly them
to a western country. They drove to the airport, forced their way on
board a large passenger jet, and found there was no pilot on board.
Terrified, they listened as the sirens got louder. Finally, one of
the scientists suggested that since he was an experimentalist, he
would try to fly the aircraft.
He sat down at the controls and tried to figure them out. The sirens
got louder and louder. Armed men surrounded the jet. The would be
pilot's friends cried out, "Please, please take off now!!!
Hurry!!!!!!"
The experimentalist calmly replied, "Have patience. I'm just a simple
pole in a complex plane."
M__________________________________________________________________________
A group of Polish tourists is flying on a small airplane through the
Grand Canyon on a sightseeing tour. The tour guide announces: "On the
right of the airplane, you can see the famous Bright Angle Falls."
The tourists leap out of their seats and crowd to the windows on the
right side. This causes a dynamic imbalance, and the plane violently
rolls to the side and crashes into the canyon wall. All aboard are
lost. The moral to this episode is: always keep your poles off the
right side of the plane.
Caveat: While this joke mentions Polish people, it is not, in my
opinion, in the category of the infamous Polish jokes. I hope no one
is offended but only humored.
M__________________________________________________________________________
Three standard Peter Lax jokes (heard in his lectures) :
1. What's the contour integral around Western Europe?
Answer: Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but
they are removable!
2. An English mathematician (I forgot who) was asked by his very religious
colleague:
Do you believe in one God?
Answer: Yes, up to isomorphism!
3. What is a compact city?
It's a city that can be guarded by finitely many near-sighted
policemen!
M__________________________________________________________________________
"Algebraic symbols are used when you do not know what you are talking about."
M__________________________________________________________________________
Q: What quantity is represented by this ?
/\ /\ /\
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
/______\ /______\ /______\
|| || ||
|| || ||
A: 9, tree + tree + tree
Q: A dust storm blows through, now how much do you have ?
A: 99, dirty tree + dirty tree + dirty tree
Q: Some birds go flying by and leave their droppings,
one per tree, how many is that ?
A: 100, dirty tree and a turd + dirty tree and a turd
+ dirty tree and a turd
M__________________________________________________________________________
Asked how his pet parrot died, the mathematician answered
"Polynomial. Polygon."
M__________________________________________________________________________
Lumberjacks make good musicians because of their natural logarithms.
M__________________________________________________________________________
From: Dr. David Batchelor batchelor@nssdca.gsfc.nasa.gov:
Theorem: Consider the set of all sets that have never been considered.
Hey! They're all gone!! Oh, well, never mind...
M__________________________________________________________________________
Pie are not square. Pie are round. Cornbread are square.
M__________________________________________________________________________
This was made by Mike Bender and Sarah Herr:
MATHEMATICS PURITY TEST
Count the number of yes's, subtract from 60, and divide by 0.6.
The Basics
1) Have you ever been excited about math?
2) Had an exciting dream about math?
3) Made a mathematical calculation?
4) Manipulated the numerator of an equation?
5) Manipulated the denominator of an equation?
6) On your first problem set?
7) Worked on a problem set past 3:00 a.m.?
8) Worked on a problem set all night?
9) Had a hard problem?
10) Worked on a problem continuously for more than 30 minutes?
11) Worked on a problem continuously for more than four hours?
12) Done more than one problem set on the same night (i.e. both
started and finished them)?
13) Done more than three problem sets on the same night?
14) Taken a math course for a full year?
15) Taken two different math courses at the same time?
16) Done at least one problem set a week for more than four months?
17) Done at least one problem set a night for more than one month
(weekends excluded)?
18) Done a problem set alone?
19) Done a problem set in a group of three or more?
20) Done a problem set in a group of 15 or more?
21) Was it mixed company?
22) Have you ever inadvertently walked in upon people doing a problem set?
23) And joined in afterwards?
24) Have you ever used food doing a problem set?
25) Did you eat it all?
26) Have you ever had a domesticated pet or animal walk over you while you
were doing a problem set?
27) Done a problem set in a public place where you might be discovered?
28) Been discovered while doing a problem set?
Kinky Stuff
29) Have you ever applied your math to a hard science?
30) Applied your math to a soft science?
31) Done an integration by parts?
32) Done two integration by parts in a single problem?
33) Bounded the domain and range of your function?
34) Used the domination test for improper integrals?
35) Done Newton's Method?
36) Done the Method of Frobenius?
37) Used the Sandwich Theorem?
38) Used the Mean Value Theorem?
39) Used a Gaussian surface?
40) Used a foreign object on a math problem (eg: calculator)?
41) Used a program to improve your mathematical technique (eg: MACSYMA)?
42) Not used brackets when you should have?
43) Integrated a function over its full period?
44) Done a calculation in three-dimensional space?
45) Done a calculation in n-dimensional space?
46) Done a change of bases?
47) Done a change of bases specifically in order to magnify your vector?
48) Worked through four complete bases in a single night (eg: using the
Graham-Schmidt method)?
49) Inserted a number into an equation?
50) Calculated the residue of a pole?
51) Scored perfectly on a math test?
52) Swallowed everything your professor gave you?
53) Used explicit notation in your problem set?
54) Purposefully omitted important steps in your problem set?
55) Padded your own problem set?
56) Been blown away on a test?
57) Blown away your professor on a test?
58) Have you ever multiplied 23 by 3?
59) Have you ever bounded your Bessel function so that the membrane
did not shoot to infinity?
69) Have you ever understood the following quote:
"The relationship between Z^0 to C_0, B_0, and H_0
is an example of a general principle which we have
encountered: the kernel of the adjoint of a linear
transformation is both the annihilator space of the
image of the transformation and also the dual space
of the quotient of the space of which the image is
a subspace by the image subspace."
(Shlomo & Bamberg's _A "Course" in Mathematics for
Students of Physics_)
M__________________________________________________________________________
From: RVFT60@email.sps.mot.com (Mike Scott)
A Cherokee indian chief had three wives, each of whom was pregnant.
The first squaw gave birth to a boy, and the chief was so elated he
built her a teepee made of buffalo hide. A few days later, the second
squaw gave birth, and also had a boy. The chief was extremely happy;
he built her a teepee made of antelope hide.
The third squaw gave birth a few days later, but the chief kept the
birth details a secret. He built the woman a teepee out of
hippopotamus hide, and challenged the people in the tribe to guess the
most recent birth details, the correct guesser receiving a fine prize.
Several of his people tried, but were unsuccessful in their guesses.
Finally, a young brave came forth and declared that the third wife had
delivered twin boys. "Correct"!, cried the chief. "How did you know"?
"It's simple", replied the warrior. "The value of the squaw of the
hippopotamus is equal to the sons of the squaws of the other two hides."
M__________________________________________________________________________
A tribe of Native Americans generally referred to their woman by the
animal hide with which they made their blanket. Thus, one woman might
be known as Squaw of Buffalo Hide, while another might be known as
Squaw of Deer Hide. This tribe had a particularly large and strong
woman, with a very unique (for North America anyway) animal hide for
her blanket. This woman was known as Squaw of Hippopotamus hide, and
she was as large and powerful as the animal from which her blanket was
made.
Year after year, this woman entered the tribal wrestling tournament,
and easily defeated all challengers; male or female. As the men of
the tribe admired her strength and power, this made many of the other
woman of the tribe extremely jealous. One year, two of the squaws
petitioned the Chief to allow them to enter their sons together as a
wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
a team. In this way, they hoped to see that she would no longer be
champion wrestler of the tribe.
As the luck of the draw would have it, the two sons who were wrestling
as a tandem met the squaw in the final and championship round of the
wrestling contest. As the match began, it became clear that the squaw
had finally met an opponent that was her equal. The two sons wrestled
and struggled vigorously and were clearly on an equal footing with the
powerful squaw. Their match lasted for hours without a clear victor.
Finally the chief intervened and declared that, in the interests of
the health and safety of the wrestlers, the match was to be terminated
and that he would declare a winner.
The chief retired to his teepee and contemplated the great struggle he
had witnessed, and found it extremely difficult to decide a winner.
While the two young men had clearly outmatched the squaw, he found it
difficult to force the squaw to relinquish her tribal championship.
After all, it had taken two young men to finally provide her with a
decent match. Finally, after much deliberation, the chief came out
from his teepee, and announced his decision. He said...
"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
of the other two hides"
M__________________________________________________________________________
A guy decided to go to the brain transplant clinic to refreshen his
supply of brains. The secretary informed him that they had three
kinds of brains available at that time. Doctors' brains were going
for $20 per ounce and lawyers' brains were getting $30 per ounce. And
then there were mathematicians' brains which were currently fetching
$1000 per ounce.
"A 1000 dollars an ounce!" he cried. "Why are they so expensive?"
"It takes more mathematicians to get an ounce of brains," she explained.
M__________________________________________________________________________
A topologist walks into a bar and orders a drink. The bartender,
being a number theorist, says, "I'm sorry, but we don't serve
topologists here."
The disgruntled topologist walks outside, but then gets an idea and
performs Dahn surgery upon herself. She walks into the bar, and the
bartender, who does not recognize her since she is now a different
manifold, serves her a drink. However, the bartender thinks she looks
familiar, or at least locally similar, and asks, "Aren't you that
topologist that just came in here?"
To which she responds, "No, I'm a frayed knot."
M__________________________________________________________________________
There are three kinds of people in the world;
those who can count and those who can't.
And the related:
There are two groups of people in the world;
those who believe that the world can be
divided into two groups of people,
and those who don't.
M__________________________________________________________________________
The world is divided into two classes:
people who say "The world is divided into two classes",
and people who say
The world is divided into two classes:
people who say: "The world is divided into two classes",
and people who say:
The world is divided into two classes:
people who say ...
M__________________________________________________________________________
What follows is a "quiz" a student of mine once showed me (which she'd
gotten from a previous teacher, etc...). It's multiple choice, and if
you sort the letters (with upper and lower case disjoint) questions
and answers will come out next to each other. Enjoy...
S. What the acorn said when he grew up
N. bisects
u. A dead parrot
g. center
F. What you should do when it rains
R. hypotenuse
m. A geometer who has been to the beach
H. coincide
h. The set of cards is missing
y. polygon
A. The boy has a speech defect
t. secant
K. How they schedule gym class
p. tangent
b. What he did when his mother-in-law wanted to go home
D. ellipse
O. The tall kettle boiling on the stove
W. geometry
r. Why the girl doesn't run a 4-minute mile
j. decagon
M__________________________________________________________________________
___ 1. That which Noah built.
___ 2. An article for serving ice cream.
___ 3. What a bloodhound does in chasing a woman.
___ 4. An expression to represent the loss of a parrot.
___ 5. An appropriate title for a knight named Koal.
___ 6. A sunburned man.
___ 7. A tall coffee pot perking.
___ 8. What one does when it rains.
___ 9. A dog sitting in a refrigerator.
___ 10. What a boy does on the lake when his motor won't run.
___ 11. What you call a person who writes for an inn.
___ 12. What the captain said when the boat was bombed.
___ 13. What a little acorn says when he grows up.
___ 14. What one does to trees that are in the way.
___ 15. What you do if you have yarn and needles.
___ 16. Can George Washington turn into a country?
A. hypotenuse I. circle
B. polygon J. axiom
C. inscribe K. cone
D. geometry L. coincide
E. unit M. cosecant
F. center N. tangent
G. decagone O. hero
H. arc P. perpendicular
M__________________________________________________________________________
A team of engineers were required to measure the height of a flag
pole. They only had a measuring tape, and were getting quite
frustrated trying to keep the tape along the pole. It kept falling
down, etc.
A mathematician comes along, finds out their problem, and proceeds to
remove the pole from the ground and measure it easily.
When he leaves, one engineer says to the other: "Just like a
mathematician! We need to know the height, and he gives us the
length!"
M__________________________________________________________________________
There was once a very smart horse. Anything that was shown it, it
mastered easily, until one day, its teachers tried to teach it about
rectangular coordinates and it couldn't understand them. All the
horse's acquaintances and friends tried to figure out what was the
matter and couldn't. Then a new guy (what the heck, a computer
engineer) looked at the problem and said,
"Of course he can't do it. Why, you're putting Descartes before the
horse!"
M__________________________________________________________________________
"The integral of e to the x is equal to f of the quantity
u to the n."
/ x n
| e = f(u )
/
M__________________________________________________________________________
TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
1. I accidentally divided by zero and my paper burst into flames.
2. Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't
actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove
that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in
and ate it.
8. I couldn't figure out whether i am the square of negative one or
i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee.
I spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but
this morning I couldn't find it.
M__________________________________________________________________________
The guy gets on a bus and starts threatening everybody: "I'll
integrate you! I'll differentiate you!!!" So everybody gets scared and
runs away. Only one person stays. The guy comes up to him and
says: "Aren't you scared, I'll integrate you, I'll differentiate
you!!!" And the other guy says; "No, I am not scared, I am e^x."
M__________________________________________________________________________
A mathematician went insane and believed that he was the
differentiation operator. His friends had him placed in a mental
hospital until he got better. All day he would go around frightening
the other patients by staring at them and saying "I differentiate
you!"
One day he met a new patient; and true to form he stared at him and
said "I differentiate you!", but for once, his victim's expression
didn't change. Surprised, the mathematician marshalled his energies,
stared fiercely at the new patient and said loudly "I differentiate
you!", but still the other man had no reaction. Finally, in
frustration, the mathematician screamed out "I DIFFERENTIATE YOU!" --
at which point the new patient calmly looked up and said, "You can
differentiate me all you like: I'm e to the x."
M__________________________________________________________________________
A function and a differentiation operator meet somewhere in
Hilbert space.
The differentation operator: Make place or I differentiate you.
Function: Forget it buster, I am e^x.
The differentation operator: Well, I am d/dy.
M__________________________________________________________________________
Boy's Life, May 1973:
Ralph: Dad, will you do my math for me tonight?
Dad: No, son, it wouldn't be right.
Ralph: Well, you could try.
M__________________________________________________________________________
Mrs. Johnson the elementary school math teacher was having children do
problems on the blackboard that day.
``Who would like to do the first problem, addition?''
No one raised their hand. She called on Tommy, and with some help he
finally got it right.
``Who would like to do the second problem, subtraction?''
Students hid their faces. She called on Mark, who got the problem but
there was some suspicion his girlfriend Lisa whispered it to him.
``Who would like to do the third problem, division?''
Now a low collective groan could be heard as everyone looked at
nothing in particular. The teacher called on Suzy, who got it right
(she has been known to hold back sometimes in front of her friends).
``Who would like to do the last problem, multiplication?''
Tim's hand shot up, surprising everyone in the room. Mrs. Johnson
finally gained her composure in the stunned silence. ``Why the
enthusiasm, Tim?''
``God said to go fourth and multiply!''
M__________________________________________________________________________
In the bayous of Louisiana, there is a small river called the Dirac.
Many wealthy people have their mansions near its mouth. One of the
social leaders decided to have a grand ball. Being a cousin of the
Governor, she arranged for a detachment of the state militia to serve
as guards and traffic directors for the big doings. A captain was
sent over with a small company; naturally he asked if there was enough
room for him and his unit. The social leader replied, "But of course,
Captain! It is well known that the Dirac delta function has unit
area."
M__________________________________________________________________________
When I was a Math/Chem grad student at Princeton in 1973-74, there was
a story going around about a grad student. This guy was always late.
One day he stumbled into class late, saw seven problems written on the
board, and wrote them down. As the week went on he began to panic:
the math department at Princeton is fiercely competitive, and here he
was unable to do most of a simple homework assignment! When the next
class rolled around he only had solved two of the problems, although
he had a pretty good idea of how to solve a third but not enough time
to complete it.
When he dejectedly flung his partial assignment on the prof's desk,
the prof asked him "What's that?" "The homework." "What homework?"
Eventually it came out that what the prof had written on the board
were the seven most important unsolved problems in the field.
This is largely an academic legend, at least according to Jan Harold
Brunvand, the author of a series of books on so-called Urban Legends.
He talks about it in his latest book _Curses! Broiled Again!_ in the
chapter entitled "The Unsolvable Math Problem." It is, however, based
in some fact. The Stanford mathematician, George B. Danzig,
apparently managed to solve two statistics problems previously
unsolved under similar circumstances.
M__________________________________________________________________________
Russell to Whitehead: "My Godel is killing me!"
M__________________________________________________________________________
"The reason that every major university maintains a department of
mathematics is that it is cheaper to do this than to institutionalize
all those people."
M__________________________________________________________________________
One attractive young businesswoman to another, over lunch:
``My life is all math. I am trying to add to my
income, subtract from my weight, divide my time,
and avoid multiplying.''
M__________________________________________________________________________
We use epsilons and deltas in mathematics because mathematicians
tend to make errors.
M__________________________________________________________________________
A mathematician decides he wants to learn more about practical
problems. He sees a seminar with a nice title: "The Theory
of Gears." So he goes. The speaker stands up and begins,
"The theory of gears with a real number of teeth is well known ..."
M__________________________________________________________________________
What keeps a square from moving ? why, square roots of course.
How many square roots does it have ? why, 2 obviously.
M__________________________________________________________________________
How can you tell that Harvard was layed out by a mathematician?
The div school [divinity school] is right next to the grad school...
M__________________________________________________________________________
First of all let me make it clear that I have nothing against
contravariant functors. Some of my best friends are cohomology
theories! But now you aren't supposed to call them contravariant
anymore. It's Algebraically Correct to call them 'differently
arrowed'!!
In the same way that transcendental numbers are polynomially
challenged?
Manifolds are personifolds (humanifolds).
Neighborhoods are neighbor victims of society.
It's the Asian Remainder Theorem.
It isn't PC to use "singularity" - the function is "convergently
challenged" there.
M__________________________________________________________________________
Godel can't prove he was here.
Descartes though he was here.
M__________________________________________________________________________
Mathematical Sex
Wherein it is related how that Polygon of Womanly Virtue, your Polly Nomial
(our heroine) is accosted by that Notorious Villain Curly Pi, and factored (oh,
horror).
Once upon a time ( 1/T ), Pretty Polly Nomial was strolling across a field of
vectors when she came to the boundary of a singularly large matrix. Now Polly
was convergent and her mother had made it an absolute condition that she never
enter such an array without her brackets on. Polly, however, who had changed her
variables that morning and was feeling particularly badly behaved, ignored this
condition on the basis that it was insufficient, and made her way amongst the
complex elements. Rows and columns closed in from all sides. Tangents approached
her surface. She became tensor and tensor. Quite suddenly, two branches of a
hyperbola touched her at a single point. She oscillated violently, lost all
sense of directrix, and went completely divergent. As she reached a turning
point, she tripped over a square root that was protruding from the erf and
plunged headlong down a steep gradient. When she rounded off once more, she
found herself inverted, apparently alone, in a non-Euclidian space.
She was being watched, however. That smooth operator, Curly Pi, was lurking
innerproduct. As his eyes devoured her curvilinear coordinates, a singular
expression crossed his face. He wondered, was she still convergent? He decided
to integrate improperly at once.
Hearing a common fraction behind her, Polly rotated and saw Curly Pi
approaching with his power series extrapolated. She could see at once by his
degenerate conic and dissipative terms that he was bent on no good.
"Arcsinh," she gasped.
"Ho, ho," he said. "What a symmetric little asymptote you have. I can see
your angles have a lot of secs."
"Oh, sir," she protested, "keep away from me. I haven't got my brackets on."
"Calm yourself, My Dear," said our Suave Operator. "Your fears are purely
imaginary."
"I, I," she thought, "perhaps he's not normal but homologous."
"What order are you?" the Brute demanded.
"Seventeen," replied Polly.
Curly leered. "I suppose you've never been operated on."
"Of course not," Polly replied quite properly. "I'm absolutely convergent."
"Come, come," said Curly, "Let's off to a decimal place I know and I'll take
you to the limit."
"Never," gasped Polly.
"Abscissa," he swore, using the vilest oath he knew. His patience was gone.
Coshing her over the coefficient with a log until she was powerless, Curly
removed her discontinuities. He stared at her significant places, and began
smoothing out her points of inflection. Poor Polly. The algorithmic method was
now her only hope. She felt his hand tending to her asymptotic limit. Her
convergence would soon be gone forever.
There was no mercy, for Curly was a heavyside operator. Curly's radius
squared itself; Polly's loci quivered. He integrated by parts. He integrated by
partial fractions. After he cofactored, he performed rungecutta on her. The
complex beast even went all the way around and did a contour integration. Curly
went on operating until he had satisfied her hypothesis, then he exponentiated
and became completely orthogonal.
When Polly got home that night, her mother noticed that she was no longer
piecewise continuous, but had been truncated in several places. But is was too
late to differentiate now. As the months went by, Polly's denominator increased
monotonically. Finally, she went to the L'Hopital and generated a small but
pathological function which left surds all over the place and drove Polly to
deviation.
The moral of our sad story is this:
'If you want to keep your expressions convergent, never allow them a single
degree of freedom...'
M__________________________________________________________________________
He thinks he's really smooth, but he's only C^1.
He's always going off on a tangent.
M__________________________________________________________________________
From: Jim Slepicka
After the earth dries out, Noah tells all the animals to 'go forth
and multiply'. However, two snakes, adders to be specific, complain to
Noah that this is one thing they have never been able to do, hard as
they have tried. Undaunted, Noah instructs the snakes to go into the
woods, make tables from the trunks of fallen trees and give it a try
on the tabletops.
The snakes respond that they don't understand how this will help them
to procreate whereupon Noah explains: "Well, even adders can multiply
using log tables!"
M__________________________________________________________________________
A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
slithering by. "Where are all the little snakes?" he asked. Mr.
Snake replied, "We are adders, so we cannot multiply."
The following year, the man returned to the same camping spot. This
time there were a whole batch of little snakes. "I thought you said
you could not multiply," he said to Mr. Snake. "Well, the park ranger
came by and built a log table, so now we can multiply by adding!"
FORMULA'S:
M__________________________________________________________________________
/
| 1
| ----- = log cabin
| cabin
/
M__________________________________________________________________________
/
| 1
| ----- = log cabin + C = houseboat
| cabin
/
M__________________________________________________________________________
8 5
If lim - = oo (infinity), then what does lim - = ?
x->0 x x->0 x
answer: (write 5 on it's side)
M__________________________________________________________________________
I saw the following scrawled on a math office blackboard in college:
1 + 1 = 3, for large values of 1
M__________________________________________________________________________
lim ----
8-->9 \/ 8 = 3
M__________________________________________________________________________
"The integral of e to the x is equal to f of the quantity
u to the n."
/ x n
| e = f(u )
/
M__________________________________________________________________________
Fuller's Law of Cosmic Irreversability:
1 pot T --> 1 pot P
but
1 pot P -/-> 1 pot T
M__________________________________________________________________________
lim sin(x)
n --> oo ------ = 6
n
Proof: cancel the n in the numerator and denominator.
M__________________________________________________________________________
From: surd@apollo.hanyang.ac.kr (ps park (Seoul Univ.))
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman) (many additions)
HOW TO PUT AN ELEPHANT INTO A REFRIGERATOR:
Analysis:
1) Differentiate it and put into the refrig.
Then integrate it in the refrig.
2) Redefine the measure on the referigerator (or the elephant).
3) Apply the Banach-Tarsky theorem.
Number theory:
1) First factorize, second multiply.
2) Use induction. You can always squeeze a bit more in.
Algebra:
1) Step 1. Show that the parts of it can be put into the refrig.
Step 2. Show that the refrig. is closed under the addition.
2) Take the appropriate universal refrigerator and get
a surjection from refrigerator to elephant.
Topology:
1) Have it swallow the refrig. and turn inside out.
2) Make a refrig. with the Klein bottle.
3) The elephant is homeomorphic to a smaller elephant.
4) The elephant is compact, so it can be put into a finite collection
of refrigerators. That's usually good enough.
5) The property of being inside the referigerator
is hereditary. So, take the elephant's mother,
cremate it, and show that the ashes fit inside the refrigerator.
6) For those who object to method 3 because it's cruel to animals.
Put the elephant's BABY in the refrigerator.
Algebraic topology:
Replace the interior of the refrigerator by its
universal cover, R^3.
Linear algebra:
1) Put just its basis and span it in the refrig.
2) Show that 1% of the elephant will fit inside the refrigerator.
By linearity, x% will fit for any x.
Affine geometry:
There is an affine transformation putting the
elephant into the refrigerator.
Set theory:
1) It's very easy!
refrigerator = { elephant }
2) The elephant and the interior of the refrigerator both have cardinality c.
Geometry:
Declare the following:
Axiom 1. An elephant can be put into a refrigerator.
Complex analysis:
Put the refrig. at the origin
and the elephant outside the unit circle.
Then get the image under the inversion.
Numerical analysis:
1) Put just its trunk and refer the rest to the error term.
2) Work it out using the Pentium.
Statistics:
1) bright statistician.
Put its tail as a sample and say "Done."
2) dull statistician.
Repeat the experiment pushing the elephant to the refrig.
3) Our NEW study shows that you CAN'T put the elephant
in the refrigerator.
M__________________________________________________________________________
Math and Alcohol don't mix, so...
PLEASE DON'T DRINK AND DERIVE
Then there's every parent's scream when their child walks into the
room dazed and staggering:
OH NO...YOU'VE BEEN TAKING DERIVATIVES!!
M__________________________________________________________________________
Q: What's purple and commutes?
A: An abelian grape.
Q: What's purple, commutes, and is worshiped by a limited number
of people?
A: A finitely venerated abelian grape.
Q: Why did the mathematician name his dog "Cauchy"?
A: Because he left a residue at every pole.
Q: Why is it that the more accuracy you demand from an interpolation
function, the more expensive it becomes to compute?
A: That's the Law of Spline Demand.
Q: What do a mathematician and a physicist [or engineer, or musician,
or whatever the profession of the person addressed] have in common?
A: They are both stupid, with the exception of the mathematician.
Q: What do you call a teapot of boiling water on top of mount everest?
A: A high-pot-in-use
Q: What do you call a broken record?
A: A Decca-gone
Q: What do you get when you cross 50 female pigs and 50 male deer?
A: One hundred sows-and-bucks
Q: Why did the chicken cross the Moebius strip?
A: To get to the other ... er, um ...
Q: What is the world's longest song?
A: "Aleph-nought Bottles of Beer on the Wall."
Q: What does a mathematician do when he's constipated?
A: He works it out with a pencil.
Q: What's yellow and equivalent to the Axiom of Choice.
A: Zorn's Lemon.
Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta.
Q: What do you get when you cross an elephant and a grape?
A: Elephant-grape-sin(theta)
Q: What do you get if you cross an elephant with a mountain climber.
A: You can't do that. A mountain climber is a scalar.
Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine theta in a direction mutually perpendicular to
the two as determined by the right hand rule.
Q: What do you get when you cross a tsetse with a mountain climber?
A: Nothing, you can't cross a vector with a scalar.
Q: To what question is the answer "9W."
A: "Dr. Wiener, do you spell your name with a V?"
Q: What's non-orientable and lives in the sea?
A: Mobius Dick.
Q: What do you get when you put a spinning flywheel in a casket and
turn a corner?
A: A funeral precession
Q: What's big, grey, and proves the uncountability of the reals?
A: Cantor's Diagonal Elephant!
Q: What do you call a young eigensheep?
A: A lamb, duh!!!
Q: What goes "Pieces of seven! Pieces of seven!"?
A: A parroty error!!
Q: What did the circle say to the tangent line?
A: "Stop touching me!"
M__________________________________________________________________________
Q: What's the title of this picture ?
.. .. ____ .. ..
\\===/======\\==
|| | | ||
|| |____| ||
|| ( ) ||
|| \____/ ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| (\ ||
|| ) ) ||
|| //||\\ ||
A: Hypotenuse
M__________________________________________________________________________
Los Angeles High School Math Exam
1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
and shoots 15 times each drive by, how many drive by shootings must he
conduct before he shoots 50 people?
2. Paul has 2 ounces of cocaine and he sells 10 grams to Jackson for $820, and
2 grams to Billy for $85 per gram. What is the street value of the balance of
the cocaine if he doesn't cut it?
3. Willie gets $200 for stealing a BMW, $50 for a Chevy and $100 for a 4x4. If
he has stolen two BMWs and three 4x4s, how many Chevys will he have to steal to
make $800?
4. If the contents of an average can of spray paint covers 22 square feet and
the average letter is eight square feet, how many letters can a teenager spray
with eight cans of paint?
5. Hector got six girls in his gang pregnant. There are 27 girls in the gang.
What percentage of girls in the gang has Hector knocked up?
6. Kathy gets $125 for sneaking an illegal alien across the border from
Mexico. She sneaked three illegals over the border every night for six days but
then one of them ripped her off for $500. How much money does she have left?
7. Byron can trade $150 worth of food stamps for two tickets to a Lakers
regular season game. If a play-off game costs 20 percent more, how many
play-off tickets can he get for $500 in food stamps?
From: jdmcmine@coop2.b11.ingr.com (Jeff)
Answers to City of Los Angeles
High School Math Proficiency Exam
1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
and shoots 15 times each drive by, how many drive by shootings must he
conduct before he shoots 50 people?
Johnny hits 15*(4/10) people per drive by, which means that he
will have to participate in 9 drive bys to shoot 50 people.
However, he will have completed two drive-by shootings and be
just starting the third when he has to reload. Since he only
stole a single clip, he'll only have shot 16 people when the
homeboys with the UZIs' make Swiss cheese out of him.
2. Pony has 2 ounces of cocaine and he sells an 8 ball to Jackson for
$320 and 2 grams to Billy for $85 per gram. What is the street value
of the balance of the cocaine if he doesn't cut it?
At 454 grams per pound, 2oz of the rock = 56.75 grams. An "8
ball" is 8 grams, so pony has sold 10 grams total and has 46.75
grams left. If he keeps selling 8-balls, he can sell 5 more (for
a total of 5*$320=$1,600) and have 6.75 grams for his own nose.
If he sells 2 gram packs, he can sell (46/2-23) packs at $85
apiece = (23*$85)=$1,955. However, he could divide it into small
parts, bake it up into crack and sell the rocks for an even
larger profit. This problem is really more suited for the Gang
Multi-Variable Economics Test.
3. Ron is pimping for 3 girls. If the price is $65 for each trick,
how many tricks will each have to turn so Ron can pay for his $800
per day crack habit.
800/$64=12 tricks plus a dance. Also, Ron should consider making
a deal with Pony from Question #2.
4. Susan wants to cut her 1/2 pound of heroin to make 20% more profit.
How many ounces of cut will she need?
If she sells the cut heroin at the same price per unit volume,
she will need 20% more volume. 20% of 1/2 pound (=8oz) is 1.6oz.
So, Susan will need 1.6oz of cut to add to the 8 oz of heroin to
get 20% more volume. She will want a cut which looks similar to
raw heroin and has approximately the same melting point. Plain
sugar or laundry detergent are suggested. Laundry detergent has
the added benefit of removing the possibility of customer
complaints, but will sharply limit repeat business.
5. Blade gets $200 for stealing a BMW, $50 for a Chevy, and $100 for
a 4x4. If he has already stolen 2BMW's and 3 4x4's, how many Chevy's
will he have to steal to make $800?
Blade has made 2*$200 + 3*$100=$700 dollars from his theft so
far. He needs $100 more, so he needs to steal $100/$50=2 more
Chevy's. However, he will probably want to steal 4 Chevy's so he
can take the extra two and make a really def low-rider.
6. Little Willy is in prison for 6 years for murder. He got $25,000
for the hit. If his common law wife is spending $250 per month, how
much money will be left when he gets out of prison and how many
years will he get for killing the bitch that spent his money?
6 years*12 months/year*$250/month=$18,000. Little Willy will
have $25,000 - $18,000 = $7,000 left when he gets out of prison.
If Little Willy kills her in the USA, he should expect to get 6
years. However, if he takes her down to Mexico and buries her
scrawny, track-marked butt in the desert, he can get off scott
free.
7. If the average can of spray paint covers 22 square feet, and
the average letter is 4 square feet, how many letters can a tagger
spray with 3 cans of paint?
3 cans of paint will cover 3*22=66 square feet. 66/4=16 letters
with a little paint left over to spray in the eyes of the cop
who's comin' after you. Or the tagger could do 15 letters and a
bitchin' skull.
8. Hector knocked up 6 girls in his gang. There are 27 girls in the
gang. What percentage of the girls in the gang has Hector knocked up?
6/27=22% of the girls. However, 2 of them are lying because
they've been sleeping with Pedro, Hector's lieutenant. So, in
actuality, Hector only knocked up 4/27 or 14.8%.
9. Rosie's sole source of income is shoplifting. If she gets 10 cents on
the dollar from her fence, how much merchandise must she shoplift each
week to make $250.
Solve X/10=250 for X, X=$2,500.
10. Mike carjacked a Chevy Camaro for his date Saturday night with his
young 14 year old girlfriend. He was arrested that night while making his
girlfriend in the backseat. How much prison time is he looking for for the
carjacking and for statutory rape, even though the girl looked legal?
Assume no prior convictions in arriving at your answer.
Mike is only 12 so he will serve no time and will be making
his girlfriend in the lot in someone else's car next Saturday.
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Why did the calculus student have so much trouble making Kool-Aid?
Because he couldn't figure out how to get a quart of water into the
little package.
M__________________________________________________________________________
A somewhat advanced society has figured how to package basic knowledge
in pill form.
A student, needing some learning, goes to the pharmacy and asks what
kind of knowledge pills are available. The pharmacist says "Here's a
pill for English literature." The student takes the pill and swallows
it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history,"
replies the pharmacist.
The student asks for these, and swallows them and has new knowledge
about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the
storeroom and brings back a whopper of a pill and plunks it on the
counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard
to swallow."
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From: a94petbe@ida.his.se (Peter Bengtsson)
In modern mathematics, algebra has become so important that
numbers will soon only have symbolic meaning.
M__________________________________________________________________________
From: sm@wf-hh.sh.sub.de (Stefan Mohr)
The shortest mathematic joke:
BEGIN -->"Epsilon less than zero"<-- END
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The law of the excluded middle either rules or does not rule, O.K.?
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Is the square root of ab absurd?
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Algebra is x-sighting.
Vectors can be 'arrowing.
I'm partial to fractions.
I like angles ... to a degree.
I could go on and on about sequences.
Translations are shifty.
Complex numbers are unreal.
I feel positive about integers.
On average, people are mean.
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From: c1prasad@watson.ibm.com (prasad)
Klein bottle for rent -- inquire within.
M__________________________________________________________________________
From: jusinkko@mail.freenet.hut.fi (jukka sinkko)
In the topologic hell the beer is packed in Klein's bottles.
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Why did the chicken cross the road?
Pierre de Fermat: I just don't have room here to give the full explanation.
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From: mstueben@pen.k12.va.us (Michael A. Stueben)
THIRTEEN MISUNDERSTANDINGS
IN THE
HISTORY OF MATHEMATICS
In the interest of historical accuracy let it be known that
...
1) Fibonacci's daughter was not named "Bunny."
2) Michael Rolle was not Danish, and did not call his
daughter "Tootsie."
3) William Horner was not called "Little-Jack" by his
friends.
4) The "G" in G. Peano does not stand for "grand."
5) Rene Descartes' middle name is not "push."
6) Isaac Barrow's middle name is not "wheel."
7) There is no such place as the University of Wis-cosine,
and if there was, the motto of their mathematics
department would not be "Secant ye shall find."
8) Although Euler is pronounced oil-er, it does not follow
that Euclid is pronounced oi-clid.
9) Franklin D. Roosevelt never said "The only thing we have
to sphere is sphere itself."
10) Fibonacci is not a shortened form of the Italian name that
is actually spelled: F i bb ooo nnnnn aaaaaaaa
ccccccccccccccccccccccccccccccccccc
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.
11) It is true that August Mobius was a difficult and
opinionated man. But he was not so rigid that he could
only see one side to every question.
12) It is true that Johannes Kepler had an uphill struggle
in explaining his theory of elliptical orbits to the
other astronomers of his time. And it is also true that
his first attempt was a failure. But it is not true that
after his lecture the first three questions he was asked
were "What is elliptical?" What is an orbit?" and "What
is a planet?
13) It is true that primitive societies use only rough
approximations for the known constants of mathematics.
For example, the northern tribes of Alaska consider the
ratio of the circumference to the diameter of a circle to
be 3. But it is not true that the value of 3 is called
Eskimo pi. Incidentally, the survival of these tribes is
dependent upon government assistance, which is not always
forthcoming. For example, the Canadian firm of Tait and
Sons sold a stock of defective compasses to the government
at half-price, and the government passed them onto the
northern natives. Hence the saying among these peoples:
"He who has a Tait's is lost."
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The History of 2 + 2 = 5
by Houston Euler
"First and above all he was a logician. At
least thirty-five years of the half-century
or so of his existence had been devoted
exclusively to proving that two and two always
equal four, except in unusual cases, where
they equal three or five, as the case may be."
-- Jacques Futrelle, "The Problem of Cell 13"
Most mathematicians are familiar with -- or have at least seen references in
the literature to -- the equation 2 + 2 = 4. However, the less well known
equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other
complex quantitiy, this history has a real part and an imaginary part; we shall
deal exclusively with the latter here.
Many cultures, in their early mathematical development, discovered the equation
2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of
South America. The Bolbs counted by tying knots in ropes. They quickly
realized that when a 2-knot rope is put together with another 2-knot rope, a
5-knot rope results.
Recent findings indicate that the Pythagorean Brotherhood discovered a proof
that 2 + 2 = 5, but the proof never got written up. Contrary to what one might
expect, the proof's nonappearance was not caused by a cover-up such as the
Pythagoreans attempted with the irrationality of the square root of two.
Rather, they simply could not pay for the necessary scribe service. They had
lost their grant money due to the protests of an oxen-rights activist who
objected to the Brotherhood's method of celebrating the discovery of theorems.
Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements,"
and nothing more was heard of 2 + 2 = 5 for several centuries.
Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after
putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with
considerably more than 4 rabbits. Fearing that too strong a challenge to the
value 4 given in Euclid would meet with opposition, Leonardo conservatively
stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his
data was roundly condemned and earned Leonardo the nickname "Blockhead." By
the way, his practice of underestimating the number of rabbits persisted; his
celebrated model of rabbit populations had each birth consisting of only two
babies, a gross underestimate if ever there was one.
Some 400 years later, the thread was picked up once more, this time by the
French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it
does." However, others objected that his argument was somewhat less than
totally rigorous. Apparently, Fermat had a more rigorous proof which was to
appear as part of a book, but it and other material were cut by the editor so
that the book could be printed with wider margins.
Between the fact that no definitive proof of 2 + 2 = 5 was available and the
excitement of the development of calculus, by 1700 mathematicians had again
lost interest in the equation. In fact, the only known 18th-century reference
to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it
in an old manuscript, wryly commented, "Well, now I know where all the departed
quantities went to -- the right-hand side of this equation." That witticism so
impressed California intellectuals that they named a university town after him.
But in the early to middle 1800's, 2 + 2 began to take on great significance.
Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean
2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an
arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great
confusion as to the actual value of 2 + 2. Because of changing opinions on
this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years
later to yield, instead, the 5-color theorem. Dedekind entered the debate with
an article entitled "Was ist und was soll 2 + 2?"
Frege thought he had settled the question while preparing a condensed version
of his "Begriffsschrift." This condensation, entitled "Die Kleine
Begriffsschrift (The Short Schrift)," contained what he considered to be a
definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand
Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved
that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned
mathematics altogether and went into university administration.
Faced with this profound and bewildering foundational question of the value of
2 + 2, mathematicians followed the reasonable course of action: they just
ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing
being done with its rival equation during the 20th century. There had been
rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first
forty pages taken up by the symbolic expression for the number five), but those
rumor remained unconfirmed. Recently, though, there have been reported
computer-assisted proofs that 2 + 2 = 5, typically involving computers
belonging to utility companies. Perhaps the 21st century will see yet another
revival of this historic equation.
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THE STORY OF BABEL:
In the beginning there was only one kind of Mathematician, created by
the Great Mathematical Spirit form the Book: the Topologist. And they
grew to large numbers and prospered.
One day they looked up in the heavens and desired to reach up as far
as the eye could see. So they set out in building a Mathematical
edifice that was to reach up as far as "up" went. Further and further
up they went ... until one night the edifice collapsed under the
weight of paradox.
The following morning saw only rubble where there once was a huge
structure reaching to the heavens. One by one, the Mathematicians
climbed out from under the rubble. It was a miracle that nobody was
killed; but when they began to speak to one another, SUPRISE of all
surprises! they could not understand each other. They all spoke
different languages. They all fought amongst themselves and each went
about their own way. To this day the Topologists remain the original
Mathematicians.
- adapted from an American Indian legend
of the Mound Of Babel
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=2.1 PROOFS:
PROOFS THAT P
(attributed to Hartry Field)
Davidson's proof that p: Let us make the following bold conjecture: p
Wallace's proof that p: Davidson has made the following bold conjecture: p
Grunbaum: As I have asserted again and again in previous publications, p.
Morgenbesser: If not p, what? q maybe?
Putnam: Some philosophers have argued that not-p, on the grounds that q.
It would be an interesting exercise to count all the fallacies in this
"argument". (It's really awful, isn't it?) Therefore p.
Rawls: It would be a nice to have a deductive argument that p from
self-evident premises. Unfortunately, I am unable to provide one. So
I will have to rest content with the following intuitive considerations
in its support: p.
Unger: Suppose it were the case that not-p. It would follow from
this that someone knows that q. But on my view, no one knows anything
whatsoever. Therefore p. (Unger beieves that the louder you say
this argument the more persuasive it becomes.)
Katz: I have seventeen arguments for the claim that p, and I know
of only four for the claim that not-p. Therefore p.
Lewis: Most people find the claim that not p completely obvious and
when I assert p they give me an incredulous stare. But the fact
that they find not-p obvious is no argument that it is true; and I
do not know how to refute an incredulous stare. Therefore p.
Fodor: My argument for p is based on three premises:
(1) q
(2) r
and
(3) p
>From these, the claim that p deductively follows.
Some people may find the third premise controversial, but it is
clear that if we replaced that premise by any other reasonable
premise, the argument would go through just as well.
Sellars's proof that p: Unfortunately, limitations of space prevent
it from being included here, but important parts of the proof can be
found in each of the articles in the attached bibliography.
Earman: There are solutions to the field equations of general
relativity in which space-time has the structure of a four-dimensional
klein bottle and in which there is no matter. In each such
space-time, the claim that not-p is false. Therefore p.
Kripke:
OUTLINE OF A "PROOF" THAT P [footnote]
Saul Kripke
Some philosophers have argued that not-p. But none of them seems to me
to have made a convincing argument against the intuitive view that
this is not the case. Therefore, p.
[footnote]. This outline was prepared hastily--at the editor's
insistence---from a taped transcript of a lecture. Since I was
not even given the opportunity to revise the first draft before
publication, I cannot be held responsible for any lacunae in the
(published version of the) argument, or for any fallacious or
garbled inferences resulting from faulty preparation of the
typescript. Also, the argument now seems to me to have problems
which I did not know when I wrote it, but which I can't discuss
here, and which are completely unrelated to any criticisms that
have appeared in the literature (or that I have seen in manuscript);
all such criticisms misconstrue the argument. It will be noted
that the present version of the argument seems to presuppose the
(intuitionistically unacceptable) law of double negation. But the
argument can easily be reformulated in a way that avoids employing
such an inference rule. I hope to expand on these matters further
in a separate monograph.
Routley and Meyer: If (q & not-q) is true, then there is a model for p.
Therefore p.
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Theorem : All positive integers are equal.
Proof : Sufficient to show that for any two positive integers, A and B,
A = B. Further, it is sufficient to show that for all N > 0, if A
and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction.
If N = 1, then A and B, being positive integers, must both be 1.
So A = B.
Assume that the theorem is true for some value k. Take A and B
with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
(A-1) = (B-1). Consequently, A = B.
M__________________________________________________________________________
From: Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly)
Theorem : All numbers are equal to zero.
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
a + b = b
a = 0
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From: Michael_Ketzlick@h2.maus.de (Michael Ketzlick)
Theorem : 3=4
Proof:
Suppose:
a + b = c
This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c
After reorganising:
4a + 4b - 4c = 3a + 3b - 3c
Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)
Remove the same term left and right:
4 = 3
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From: Benjamin.J.Tilly@dartmouth.edu (Benjamin J. Tilly)
Theorem: 1$ = 1c.
Proof:
And another that gives you a sense of money disappearing...
1$ = 100c
= (10c)^2
= (0.1$)^2
= 0.01$
= 1c
Here $ means dollars and c means cents. This one is scary in that I
have seen PhD's in math who were unable to see what was wrong with this
one. Actually I am crossposting this to sci.physics because I think
that the latter makes a very nice introduction to the importance of
keeping track of your dimensions...
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From: clubok@physics11 (Kenneth S. Clubok)
Theorem: 1 = -1 .
Proof:
1 -1
-- = --
-1 1
1 -1
sqrt[ -- ] = sqrt[ -- ]
-1 1
sqrt[1] sqrt[-1]
------- = -------
sqrt[-1] sqrt[1]
1=-1 (by cross-multiplication)
And here's my personal favorite:
Use integration by parts to find the anti-derivative of 1/x. One
can get the amusing result that 0=1. (Until you realize you have to put
in the limits.)
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From: jreimer@aol.com (JReimer)
Theorem: 1 = -1
Proof:
1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1
Also one can disprove the axiom that things equal to the same thing
are equal to each other.
1 = sqrt(1)
-1 = sqrt(1)
therefore 1 = -1
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From: kdq@marsupial.jpl.nasa.gov (Kevin D. Quitt)
Theorem: 4 = 5
Proof:
16 - 36 = 25 - 45
4^2 - 9*4 = 5^2 - 9*5
4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4
(4 - 9/2)^2 = (5 - 9/2)^2
4 - 9/2 = 5 - 9/2
4 = 5
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baez@guitar.ucr.edu (john baez) writes:
Theorem: 1 + 1 = 2
Proof:
n(2n - 2) = n(2n - 2)
n(2n - 2) - n(2n - 2) = 0
(n - n)(2n - 2) = 0
2n(n - n) - 2(n - n) = 0
2n - 2 = 0
2n = 2
n + n = 2
or setting n = 1
1 + 1 = 2
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From: magidin@uclink.berkeley.edu (Arturo Viso Magidin)
Theorem: In any finite set of women, if one has blue eyes then they
all have blue eyes.
Proof. Induction on the number of elements.
if n= or n=1 it is immediate.
Assume it is true for k
Consider a group with k+1 women, and without loss of generality assume
the first one has blue eyes. I will represent one with blue eyes with
a '*' and one with unknown eye color as @.
You have the set of women:
{*,@,...,@} with k+1 elements. Consider the subset made up of the first
k. This subset is a set of k women, of which one has blue eyes. By
the induction hypothesis, all of them have blue eyes. We have then:
{*,...,*,@}, with k+1 elements. Now consider the subset of the last k
women. This is a set of k women, of which one has blue eyes (the next-to-last
element of the set), hence they all have blue eyes, in particular
the k+1-th woman has blue eyes.
Hence all k+1 women have blue eyes.
By induction, it follows that in any finite set of women, if one has
blue eyes they all have blue eyes. QED
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From: Zorro
Theorem:
All positive integers are interesting.
Proof:
Assume the contrary. Then there is a lowest non-interesting positive
integer. But, hey, that's pretty interesting! A contradiction.
QED
I heard this one from G. B. Thomas, but I don't know whether it is due to
him.
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From: daniel@hagar.ph.utexas.edu (James Daniel)
Aren't multi-valued functions fun? Once you realize what's going on,
though, you can make them into silly proofs pretty much without thinking.
Here's one I just made up:
Object: to prove that i < 0 ( that is, sqrt(-1) < 0 )
Well, ( .5 + sqrt(3/4)*i )^3 = (-1)^3
(most would assert this to be a false statement -- mostly
cuz they'll get the math wrong. It's a true statement.
It's the next statement that is false.)
which means that .5 + sqrt(3/4)*i = -1
So then 1 + sqrt(3)*i = -2
sqrt(3)*i = -1
i = -1/sqrt(3)
Therefore i is a negative number. QED.
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From: julison@cco.caltech.edu (Julian C. Jamison)
Theorem: All numbers are equal.
Proof:
Choose arbitrary a and b, and let t = a + b. Then
a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
(a - t/2)^2 = (b - t/2)^2
a - t/2 = b - t/2
a = b
So all numbers are the same, and math is pointless.
M__________________________________________________________________________
From: pfc@math.ufl.edu (P. Fritz Cronheim)
This one is from Jerry King's _Art of Mathematics_
16/64=1/4 by cancelling the 6's. Here the result is true, but the method
is not. Do the ends justify the means? :)_
M__________________________________________________________________________
Methods of Mathematical Proof
This is from _A Random Walk in Science_ (by Joel E. Cohen?):
To illustrate the various methods of proof we give an example of a
logical system.
THE PEJORATIVE CALCULUS
Lemma 1. All horses are the same colour.
(Proof by induction)
Proof. It is obvious that one horse is the same colour. Let us assume
the proposition P(k) that k horses are the same colour and use this to
imply that k+1 horses are the same colour. Given the set of k+1 horses,
we remove one horse; then the remaining k horses are the same colour,
by hypothesis. We remove another horse and replace the first; the k
horses, by hypothesis, are again the same colour. We repeat this until
by exhaustion the k+1 sets of k horses have been shown to be the same
colour. It follows that since every horse is the same colour as every
other horse, P(k) entails P(k+1). But since we have shown P(1) to be
true, P is true for all succeeding values of k, that is, all horses are
the same colour.
Theorem 1. Every horse has an infinite number of legs.
(Proof by intimidation.)
Proof. Horses have an even number of legs. Behind they have two legs
and in front they have fore legs. This makes six legs, which is cer-
tainly an odd number of legs for a horse. But the only number that is
both odd and even is infinity. Therefore horses have an infinite num-
ber of legs. Now to show that this is general, suppose that somewhere
there is a horse with a finite number of legs. But that is a horse of
another colour, and by the lemma that does not exist.
Corollary 1. Everything is the same colour.
Proof. The proof of lemma 1 does not depend at all on the nature of the
object under consideration. The predicate of the antecedent of the uni-
versally-quantified conditional 'For all x, if x is a horse, then x is
the same colour,' namely 'is a horse' may be generalized to 'is anything'
without affecting the validity of the proof; hence, 'for all x, if x is
anything, x is the same colour.'
Corollary 2. Everything is white.
Proof. If a sentential formula in x is logically true, then any parti-
cular substitution instance of it is a true sentence. In particular
then: 'for all x, if x is an elephant, then x is the same colour' is
true. Now it is manifestly axiomatic that white elephants exist (for
proof by blatant assertion consult Mark Twain 'The Stolen White Ele-
phant'). Therefore all elephants are white. By corollary 1 everything
is white.
Theorem 2. Alexander the Great did not exist and he had an infinite
number of limbs.
Proof. We prove this theorem in two parts. First we note the obvious
fact that historians always tell the truth (for historians always take
a stand, and therefore they cannot lie). Hence we have the historically
true sentence, 'If Alexander the Great existed, then he rode a black
horse Bucephalus.' But we know by corollary 2 everything is white;
hence Alexander could not have ridden a black horse. Since the conse-
quent of the conditional is false, in order for the whole statement to
be true the antecedent must be false. Hence Alexander the Great did not
exist.
We have also the historically true statement that Alexander was warned
by an oracle that he would meet death if he crossed a certain river. He
had two legs; and 'forewarned is four-armed.' This gives him six limbs,
an even number, which is certainly an odd number of limbs for a man.
Now the only number which is even and odd is infinity; hence Alexander
had an infinite number of limbs. We have thus proved that Alexander the
Great did not exist and that he had an infinite number of limbs.
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Theorem: a cat has nine tails.
Proof: No cat has eight tails. A cat has one tail more than no cat.
Therefore, a cat has nine tails.
M__________________________________________________________________________
From: rmaimon@husc9.Harvard.EDU (Ron Maimon)
Theorem: All dogs have nine legs.
Proof:
would you agree that no dog has five legs?
would you agree that _a_ dog has four legs more then _no_ dog?
4 + 5 = ?
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=2.2 STATISTICS AND STATISTICANS:
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Did you hear the one about the statistician?
Probably....
M__________________________________________________________________________
Statistics means never having to say you're certain.
[With apologies to Erich Segal]
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In earlier times, they had no statistics, and so they had to fall
back on lies. - STEPHEN LEACOCK
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