Apr 292010

In what may be the simplest and most elegant formula of all time, Leonhard Euler discovered the relationship between all of the most elemental and primal constants in our mathematical system.  Sometimes called Euler’s Identity, it isn’t a very useful formula because there aren’t any variables in the equation, but you have to admit, it is amazing.  No other formula can claim to combine and relate so many of the most important numbers is such a simple way.

e^{i \pi} + 1 = 0

Look at it.  Ain’t it beautiful?  It’s got:

The constant e (2.718..)

The constant \pi (3.141..)

The constant i (i is the square root of -1)

The constant 1

The constant 0

And the mathematical operations of addition, multiplication, and exponentiation.

One simple equation that pulls it all together.  Who would have thought?  Euler, that’s who.  Good job.  I’m impressed.

More information on wikipedia.