The angles of a triangle drawn on a sphere add to more than one hundred eighty degrees, unlike flat triangles.

The longer version

Run two lines of longitude from the pole down to the equator, separated by a quarter turn, and close the shape along the equator. Every corner is a right angle, so the three add to two hundred seventy degrees rather than the familiar flat total. Curvature supplies the surplus.

The overshoot is not random: it grows in step with the area enclosed, so measuring angles on a sphere amounts to measuring the patch they cover. Pilots and ship navigators meet this whenever routes follow great circles. Shrink the triangle and the excess fades toward nothing, which is why everyday geometry on a pavement works fine.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.