What is Euler's Identity?
Euler's identity is named after genius mathematician Leonhard Euler. It is considered to be the most beautiful mathematical equation.
If you haven't, take a moment to really look at it and realize how extraordinary this is.This formula claims that e (the base of the natural logarithm, an irrational number) raised to the power π (relating circle circumference to diameter, also irrational) times an imaginary number is not only meaningful, but it's a real whole number: negative one.
This is a mind-bending assertion. An irrational raised to the power of an imaginary irrational is somehow equal to negative one?
Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: The number 0, the additive identity. The number 1, the multiplicative identity. The number π, which is ubiquitous in the geometry of Euclidean space and analytical mathematics (π = 3.141...) The number e, the base of natural logarithms, which occurs widely in mathematical analysis (e = 2.718...). The number i, the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials (that are not constants), and whose study leads to deeper insights into many areas of algebra and calculus. Stanford University mathematics professor Keith Devlin has said, "like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence".
