Euler`s Identity, The Code Of The Universe.

There was a poll voted by mathmaticians, that asked for their favourite equation ever. This may seem like a silly question for such a practical subject as maths, but the result spoke volumes.

And here it is: e^i(pi) + 1 = 0, (e) to the power of (i) times (pi) is equal to minus one.

known as Euler`s theorem.

It marries together three important numbers in maths; one of which is irrational (meaning a number with a decimal which goes on forever pi = 3.147......) and comes from circular geometry, another is imaginary ( created to keep 2 solutions going in quadratic equations i = the square root of minus 1), and finally a convenient number created for calculus work ( e to the power of any number (e.g. e^x) differentiated or integrated is still e^x).

But put together in such a simple way they make a real and simple number minus 1. This format laid the foundations for varied and important areas in maths and science, from basic geometry to quantum mechanics.

without knowing it you have almost certainly used it yourselves in the form of the trigonometric functions: cos and sin.

sin = (e^ix - e^-ix) / 2i

cos = (e^ix - e^ix) / 2

where the angle x is converted into radians in your calculator from degrees where 360 degrees is equal to 2 pi radians.

sin and cos make the perfect wave shape when plotted into a graph, we can then use them in studying waves in physics.

The amplitude at position x and time t is = A cos(kx - wt).

w= frequency f times 2pi, and k is 2 pi divided by the wavelength.

Or otherwise expressed as the real part of: e^i(kx - wt).

which is also used to describe the probability of the position of a particle in quantum physics.

It is therefore the keystone that so much maths and science branches out from and depends on, as well as being so surprising and elegant.