Pi minima

The Pythagorean theorem states that `a^2 + b^2 = c^2`. But what if we generalise this formula to `a^n + b^n = c^n`? By changing `n` we can describe different, non-Euclidean spaces. A circle is defined as a series of points equidistant from its center, so the formula of a unit circle is `x^2 + y^2 = 1`, and in case you forgot what a circle looks like, it looks like this:

But if we live in a world where `n != 2`, what does a circle look like? here's `n = 1`.