#geometry

Pi is the ratio of a circle's circumference to its diameter. It's 3.14159... because that's how circles work, and the value is the same in every universe with circles.

The Law of Sines is the cleanest result in triangle trigonometry. The ratio of any side to the sine of its opposite angle is the same for all three sides. The proof is one line, and the consequences are surprising.

The Pythagorean theorem only works on right triangles. The Law of Cosines is the generalization that works on any triangle, with one extra term that captures the angle.

The Pythagorean theorem is the result every middle-schooler memorizes and most adults never see proven. The classic proof using rearranged squares is one of the cleanest mathematical arguments ever made.