Why e^(iπ) + 1 = 0 — Euler's Identity visualized #shorts #euler #projecteuler

本站添加: 2026-05-16

[00:00:00]Five constants, zero, one, pi, i, and e.

[00:00:06]They come from totally different worlds.

[00:00:08]One equation puts them together. E to the i pi plus one equals zero.

[00:00:14]Start at one on the unit circle. As theta grows, e to the i theta walks counterclockwise around the circle. E to the i pi means halfway around. You land at minus one.

[00:00:27]Add one, you land at zero. That's the identity. Rotation by pi plus a step of one returns to the origin.

[00:00:35]Why does e do this? Because e to the i theta means cosine theta plus i sine theta. The real part is a cosine wave, the imaginary part a sine wave.

[00:00:47]Together, they trace a circle.

[00:00:50]Five constants, one equation, often called the most beautiful in mathematics.