What is the most elegant theorem/proof? (1 Viewer)

[Euler]

There has been nothing about it in this forum, even though it is titled "Appreciating the Beauty and Elegance".

So here goes.

Mine is a toss up between proofs of irrationality of sqrt(2) and the infinite number of primes via Euclid.

 

[McLake]

I like the proof that e^(i*(pi)) = -1. It's just so quirky ...

 

[freaking_out]

Originally posted by McLake
I like the proof that e^(i*(pi)) = -1. It's just so quirky ...

yeah, that formula(e^(i*(pi))+1=0) , basically has all the "special" symbols of mathematics, i.e pi, e, i, 1, 0.

 

[McLake]

Originally posted by freaking_out
yeah, that formula(e^(i*(pi))+1=0) , basically has all the "special" symbols of mathematics, i.e pi, e, i, 1, 0.

Well, it's more the fact that it links the calculas, polynomial, trig, log and complex branches of maths ...

 

[freaking_out]

Originally posted by drbuchanan
We now know from recent 4 unit papers that e and pi are irrational.

Did you know that

is also irrational?

It follows from Gelfond's theorem:

http://mathworld.wolfram.com/GelfondsTheorem.html

lol- so u reckon thats gonna come up on this years paper?