Euler+graph : Ataahua

e^{i π} + 1 = 0
(say "E to the power of i pi, plus one, equals zero")

This equation, by Leonhard Euler (say "oiler"), 1707-1783, is widely regarded as the most beautiful in all mathematics. Called "Euler's identity", it relates the numbers 1, 0, e (2.71828..., the base of natural logarithms), Π (3.141592..., the ratio of a circle's diameter to its circumference) and i (the square root of minus 1, the basis of the "imaginary" numbers) - numbers nobody expected to be related. And it unites the relations of addition, multiplication, exponention and equation, all in a few elegant symbols.

This version is accompanied by an elegant graph of the equation, on a complex plane (an Argand diagram). Imaginary numbers are measured upward. The curve starts at e⁰=1 and goes with velocity i till it reaches p, then in a straight line to 0.

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