The Sum of Interior Angles: 180°

The angles of any triangle in Euclidean geometry sum to exactly 180°. The proof is elegant: draw a line through the apex parallel to the base; the three angles at that line equal the triangle's angles by alternate interior angles. But in spherical geometry, triangle angles sum to more than 180°: a triangle from the North Pole to two points on the equator 90° apart has three right angles — summing to 270°. In hyperbolic geometry, triangle angles sum to less than 180°. The number 180° is not a universal truth but a signature of flat space.