The Greeks didn’t impose arbitrary rules just to make math more challenging. The game of constructing shapes with a compass and straightedge originates in Euclid’s Elements from the third century B.C.E., one of the most important textbooks ever written. Like modern mathematicians, Euclid set out to derive all of geometry from a minimal list of assumptions. Instead of merely asserting the existence of shapes or other geometric objects, Euclid wanted to build them explicitly from the simplest ingredients: lines and circles. To get a feel for these constructions, try one for yourself: find the midpoint of the line segment from A to B below. Eyeballing won’t suffice; your method must identify the exact midpoint.