I think that the biggest mistake in the pedagogy of high-school geometry is how we teach the trigonometric functions (sine, cosine, etc). We tell people that these functions are about triangles, and spend a lot of time in classes finding the missing sides and angles in triangles. But they these functions aren’t about triangles at all! They’re about circles, and it just happens that triangles are about circles as well, since just about everything is about circles.This is why π appears in ...
