Curved space Memes

Euclidean geometry crying in the corner while non-Euclidean geometry flexes with its mind-bending rules! In standard Euclidean geometry, an equilateral triangle (all sides equal) can't also be a right triangle (one 90° angle) because angles in a triangle must sum to 180°. But switch to a spherical surface and suddenly geometry goes wild! On a sphere, you can create a triangle with three 90° angles—adding up to 270°—completely breaking Euclidean rules. That spherical diagram is literally showing how triangles on curved surfaces can have properties that would make your high school geometry teacher have an existential crisis.

Euclidean geometry lies in shambles as two bugs on a sphere completely wreck the concept of parallel lines! The top panel shows our confident mathematician declaring "their trajectories will never cross" about two insects walking along what appear to be parallel lines on a grid. But the bottom panel reveals the brutal truth - on a curved surface like a sphere, those "parallel" lines inevitably converge at the poles. Non-Euclidean geometry strikes again! It's like telling someone their relationship is going nowhere and then watching them get married. Geometry professors are quietly sobbing right now.