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!
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Q: How many numerical analysts does it take to screw in a light bulb?
A: 0.9973 after the first three iterations.
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Some say the pope is the greatest cardinal.
But others insist this cannot be so, as every pope has a successor.
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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.
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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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Theorem: 1$ = 1c.
Proof:
And another that gives you a sense of money disappearing...
1$ = 100c
= (10c)^2
= (0.1$)^2
= 0.01$
= 1c
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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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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
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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.
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Prove that the crocodile is longer than it is wide.
Lemma 1. The crocodile is longer than it is green:
Let's look at the crocodile. It is long on the top and on the bottom, but it is
green only on the top. Therefore, the crocodile is longer than it is green.
Lemma 2. The crocodile is greener than it is wide:
Let's look at the crocodile. It is green along its length and width, but it is
wide only along its width. Therefore, the crocodile is greener than it is wide.
>From Lemma 1 and Lemma 2 we conclude that the crocodile is longer than it is
wide.
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"A mathematician is a device for turning coffee into theorems"
-- P. Erdos
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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.
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My geometry teacher was sometimes acute, and sometimes
obtuse, but always, he was right.
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"Aleph-0 bottles of beer on the wall,
Aleph-0 bottles of beer;
Take one down, pass it around,
Aleph-0 bottles of beer on the wall!
Aleph-0 bottles of beer on the wall..."
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One bottle of beer on the wall
One bottle of beer on the wall
if this bottle MAY fall
there is a half bottle of beer on the wall
(assuming equiprobability, of course)
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If you can solve a literal equation
And rationalise denominator surds,
Do grouping factors (with a transformation)
And state the factor theorem in words;
If you can plot the graph of any function
And do a long division (with gaps),
Or square binomials without compunction
Or work cube roos with logs without mishaps.
If you possess a sound and clear-cut notion
Of interest sums with P and I unknown;
If you can find the speed of trains in motion,
Given some lengths and "passing-times" alone;
If you can play with R (both big and little)
And feel at home with l (or h) and Pi,
And learn by cancellation how to whittle
Your fractions down till they delight the eye.
If you can recognise the segment angles
Both at the centre and circumference;
If you can spot equivalent triangles
And Friend Pythagoras (his power's immmense);
If you can see that equiangularity
And congruence are two things and not one,
You may pick up a mark or two in charity
And, what is more, you may squeeze through, my son.
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This poem was written by Jon Saxton (an author of math textbooks).
((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
Or for those who have trouble with the poem:
A Dozen, a Gross and a Score,
plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more.
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'Describe the universe (max. 200 words) and give three examples.'
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Heisenberg might have slept here.
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Ivan Ivanovich, great russian Scientist does an experiment. He wants
to know how fast a thermometer falls down. He takes a thermometer and
a light, a candle light. He drops both from the 3rd floor and recognices
that they are reaching the ground at the same time. Ivan Ivanovich, great
russian scientific writes in his book: A theomometer falls with the speed
of light.
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HEAVEN IS HOTTER THAN HELL
The temperature of Heaven can be rather accurately computed. Our
authority is Isaiah 30:26, "Moreover, the light of the Moon shall be as
the light of the Sun and the light of the Sun shall be sevenfold, as
the light of seven days." Thus Heaven receives from the Moon as much
radiation as we do from the Sun, and in addition 7*7 (49) times as much
as the Earth does from the Sun, or 50 times in all. The light we
receive from the Moon is one 1/10,000 of the light we receive from the
Sun, so we can ignore that ... The radiation falling on Heaven will
heat it to the point where the heat lost by radiation is just equal to
the heat received by radiation, i.e., Heaven loses 50 times as much
heat as the Earth by radiation. Using the Stefan-Boltzmann law for
radiation, (H/E)^4 = 50, where E is the absolute temperature of the
earth (300K), gives H as 798K (525C). The exact temperature of Hell
cannot be computed ... [However] Revelations 21:8 says "But the
fearful, and unbelieving ... shall have their part in the lake which
burneth with fire and brimstone." A lake of molten brimstone means
that its temperature must be at or below the boiling point, 444.6C. We
have, then, that Heaven, at 525C is hotter than Hell at 445C.
-- From "Applied Optics" vol. 11, A14, 1972
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Whatever the temperature of hell, I can prove that it is isothermal.
We must begin by assuming that there is at least one physicist in hell. Most
of us can think of a particular example.
Now assume that some portion of hell is out of equilibrium, a bit hotter or
colder than the rest. If so, then that physicist would build a heat engine
and extract some energy, and use that energy to run a refrigerator. He would
cool some other part of hell down until it was comfortable.
But it is contrary to the definition of hell that any part of it should be
comfortable. QED.
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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 ...
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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.
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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
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TOP TEN EXCUSES FOR NOT DOING A 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.
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What keeps a square from moving ? why, square roots of course.
How many square roots does it have ? why, 2 obviously.
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How can you tell that Harvard was layed out by a mathematician?
The div school [divinity school] is right next to the grad school...
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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!"
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lim ----
8-->9 \/ 8 = 3
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In 1960: A logger sells a truckload of lumber for $100. His cost
of production is four-fifths of this price. What is his profit?
In 1970: A logger sells a truckload of lumber for $100. His cost
of production is four-fifths of this price, or $80. What is his
profit?
In 1970 (new math): A logger exchanges a set L of lumber for a set
M of money. The cardinalitiy of set M is 100, and each element is
worth $1.00. Make 100 dots representing the elements of the set M.
The set C of the costs of production contains 20 fewer points than
set M. Represent the set C as a subset of M, and answer the
following question: What is the cardinality of the set P of points?
In 1980: A logger sells a truckload of wood for $100. His cost of
production is $80, and his profit is $20. Your assignment:
underline the number 20.
In 1990 (outcome-based education): By cutting down beautiful forest
trees, a logger makes $20. What do you think of this way of making
a living? (Topic for class participation: How did the forest birds
and squirrels feel?)