Motion Beyond the Elements

Doing mathematics is often rather similar to playing a well-defined game. Book I of Euclid’s ElementsEuclid’s Elements gives us a beautiful example. I call it the Euclidean construction game. The Postulates 1 through 3 give us the rules of the game, the permitted ideal movements. The famous problems, the squaring of the circleSquaring of the circle, the doubling of the cubeDoubling of the cube and the trisectionTrisectionof any angle of any angle, could not be solved using only the postulates 1 through 3. Trying to solve these anomalous problems anyway Greek mathematicians were experimenting with other means to execute constructions, all of them based on motion.