## Geometry

Ya’ hear about the geometer who went to the beach to catch the rays and became a tangent ?

My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.

## Proof:All odd integers are prime.

Well, the first student to try to do this was a math student. Hey says “hmmm… Well, 1 is prime, 3 is prime, 5 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, 1 is prime, 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… 1 is prime, 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….”

## Lemma:All horses are the same color.

Proof (by induction):

Case n=1: In a set with only one horse, it is obvious that all horses in that set are the same color.

Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same color. Then the set of k+1 horses are all the same color. We have k true => k+1 true; therefore all horses are the same color.

Theorem: All horses have an infinite number of legs.

Proof (by intimidation):

Everyone would agree that all horses have an even number of legs. It is also well-known that horses have forelegs in front and two legs in back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a horse to have! Now the only number that is both even and odd is infinity; therefore all horses have an infinite number of legs.

However, suppose that there is a horse somewhere that does not have an infinite number of legs. Well, that would be a horse of a different color; and by the Lemma, it doesn’t exist.

## What is “pi”?

Mathematician: Pi is thenumber expressing the relationship between the circumference of a circle and its diameter.

Physicist: Pi is 3.1415927plus or minus 0.000000005

Engineer: Pi is about 3.

## Noah’s Ark

The ark lands after The Flood. Noah lets all the animals out. Says, “Go and multiply.” Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. “What’s the problem?” says Noah. “Cut down some trees and let us live there”, say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, “Want to tell me how the trees helped?” “Certainly”, say the snakes. “We’re adders, and we need logs to multiply.”

## The story of Babel

In the beginning there was only one kind of Mathematician, created by the Great Mathamatical 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 suprises! 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

## 1 + 1 = 1

(I’m not sure if the following one is a true story or not) The great logician Betrand Russell (or was it A.N. Whitehead?) once claimed that he could prove anything if given that 1+1=1. So one day, some smarty-pants asked him, “Ok. Prove that you’re the Pope.” He thought for a while and proclaimed, “I am one. The Pope is one. Therefore, the Pope and I are one.”

## Three men in a hot-air balloon

Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, “I’ve got an idea. We can call for help in this canyon and the echo will carry our voices far.” So he leans over the basket and yells out, “Helllloooooo! Where are we?” (They hear the echo several times). 15 minutes later, they hear this echoing voice: “Helllloooooo! You’re lost!!” One of the men says, “That must have been a mathematician.” Puzzled, one of the other men asks, “Why do you say that?” The reply: “For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless.”

## Two men

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.