By Per

1

Posted: 2013-07-07

Euler's identity

Euler's identity

$$$e^{i \pi}+1=0$$$

This is one of the most famous equations in all of mathematics. Its especially nice since it involves a large number of different central objects such as 0, 1, i, $$pi$$, $$e$$. The identity can be proved using that any given exponential $$e^{ix}$$ can be written as $$ e^{ix}=cos x + i sin x $$ for some real number x.