Why is it so pretty?
$$ e^{i\pi} + 1 = 0 $$- $e$ is Euler’s number, the base of natural logarithms
- $i$ is the imaginary unit, which by definition satisfies $i^2 = -1$
- $\pi$ is pi, the ratio of the circumference of a circle to its diameter
Euler’s Identity is a special case of Euler’s formula evaluated for $x = \pi$:
$$e^{ix} = \cos{x} + i\sin{x}$$It is an especially beautiful result in math because it relates five fundamental numbers in mathematics ($0, 1, e, \pi, i$) with the three most common operators in math (addition, multiplication, exponentiation).
References
- Project Euler: a website where you can play math puzzles for fun. After I got bored from mastering Sudoku (a fun game on paper, but computers that enable full record keeping for each box makes the game too easy), the next best game is just math!
- Lockhart’s Lament - Math can really be a beautiful subject.
“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” -Keith Devlin