1. Amazing math forumlae

Hello all, are there any formulae that mathematicians love for any particular reason? I think I remember someone saying that

$\displaystyle e^i\pi+1=0$ is some kind of magical thing. Sorry if I'm being totally random but it's something like that and people say it's stuff like this that makes math magical...

are there any other formulae that make maths "magical"

2. Re: Amazing math forumlae

You are right
this formula discovered by Euler is a magic formula connecting all known units ,zero and the magic numbers π and e .
Minoas

3. Re: Amazing math forumlae

Originally Posted by uperkurk
$\displaystyle e^{i\pi}+1=0$ is some kind of magical thing. Sorry if I'm being totally random but it's something like that and people say it's stuff like this that makes math magical...
are there any other formulas that make maths "magical"
There are no magical formulas in mathematics.

Originally Posted by MINOANMAN
You are right
this formula discovered by Euler is a magic formula connecting all known units ,zero and the magic numbers π and e .
Nonsense! Mathematics is the product of the brain. Note that I did not say 'human brain'. There is a well respected book by The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene.

The history of mathematics is fascinating. The number zero was not accepted for years: the is a year 1BCE and a year 1CE but no year zero. If fact, we think that the symbol 0 was adopted because that is the impression left when a counting stone was removed from a counting table made of sand.

Negative numbers have had a troubled history not even to mention irrational numbers.

Therefore, there was a real debate about complex numbers. We wanted to extend as many properties of real numbers to complex numbers as possible.

To that end if $\displaystyle x$ is a real number, define $\displaystyle e^{ix}=\cos(x)+i\sin(x)$. Thus it is perfectly clear that $\displaystyle e^{i\pi}=-1$.

There is no magic there. It is just a definition extending definitions for real numbers to complex numbers in such a way to make them consistent.

4. Re: Amazing math forumlae

This identity always makes me chuckle.

. . $\displaystyle (1 +2+3+\cdots+n)^2 \:=\;1^3+2^3+3^3 +\cdots+ n^3$

And I love this "sequence":

. . $\displaystyle \begin{array}{ccc}3^2+4^2 &=& 5^2 \\ 3^3+4^3+5^3 &=& 6^3 \\ \vdots && \vdots \end{array}$

5. Re: Amazing math forumlae

Stokes' theorem, one of the most beautiful in mathematics:

$\displaystyle \int_{\partial \Omega}\omega=\int_{\Omega}\mathrm {d}\omega$

6. Re: Amazing math forumlae

I think you are referring to Richard Feynman saying $\displaystyle e^{i\pi} + 1 = 0$ is the most beautifu of abstract algebra facsinates me l equation because it includes transcendental, natural numbers, with addition, multiplication and exponentiation.(Someone else probably said it as well, but since Feynman was such a popularizer of science, i think most people probably heard it from him, including me).

For me, its not a thrm but the massive role that poylnomials and their roots have in modern algebra is just fascinating.

7. Re: Amazing math forumlae

Originally Posted by jakncoke
I think you are referring to Richard Feynman saying $\displaystyle e^{i\pi} + 1 = 0$ is the most beautiful equation because it includes transcendental, natural numbers, with addition, multiplication and exponentiation.
But why? Why does it mean?

8. Re: Amazing math forumlae

Originally Posted by uperkurk
But why? Why does it mean?
I don't know friend, the answer to your question lies more with "what is beauty" rather than some innate property of that equality.