# I'm in a talent show tomorrow. Show me a cool math proof.

## Main Question or Discussion Point

I thought about doing a proof of the Pythagorean Theorem, a proof that the harmonic series is unbounded, a proof that e^π > π^e, a proof that e^(b*i) = cos(b) + i*sin(b), a proof that √2 is irrational, but honestly, none of those are cool enough.

Please show me a cool proof that an ordinary audience could understand.

## Answers and Replies

Maybe a proof of Euclid's theorem of the infinitude of primes, or a proof of Euler's identity..?

chiro
Monty Hall Problem - its not intuitive and a lot of people (even including statisticians) can doubt the results even due to its counter intuitiveness

Monty Hall Problem - its not intuitive and a lot of people (even including statisticians) can doubt the results even due to its counter intuitiveness
hmmmm .... the only problem with the Monty Hall Problem is that the setup is hard to explain. You have to explain to rules of the game 4 or 5 times before the audience understands how it works.

chiro
hmmmm .... the only problem with the Monty Hall Problem is that the setup is hard to explain. You have to explain to rules of the game 4 or 5 times before the audience understands how it works.
What kind of audience are you speaking to?

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that is really pretty cool

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mathwonk
Homework Helper
describe 4 dimensional spheres?

describe 4 dimensional spheres?
no u

A simple Diophantine equation? a^b=b^a is fun, and pretty easy to understand. It also has the attribute of not being part of any curriculum, so even the advanced audience members won't know the answer until you prove it. (unless they are fast)

A simple Diophantine equation? a^b=b^a is fun, and pretty easy to understand. It also has the attribute of not being part of any curriculum, so even the advanced audience members won't know the answer until you prove it. (unless they are fast)
is there someway to solve this algorithmically? without just seeing that it's 2 and 4?

Landau
How does reproducing a proof given by someone on this forum show that you have talent? I mean, doesn't this defeat the purpose of a talent show?

How does reproducing a proof given by someone on this forum show that you have talent? I mean, doesn't this defeat the purpose of a talent show?
> Implying that talent and originality are the same thing.

LCKurtz
Homework Helper
Gold Member
You could entertain them with non-proofs of true theorems. One of my favorites is the "long division" method proving the remainder of a polynomial p(x) upon division by (x - a ) is p(a)

Proof
Code:
         p
_______________
(x-a)/  p(x)
p(x) - p(a)
__________

p(a)