Napoleon's Problem

Napoleon's problem is a famous compass construction problem. In it, a circle and its center are given. The challenge is to divide the circle into four equal arcs using only a compass. Napoleon was known to be an amateur mathematician but it is not known if he either created or solved the problem. Napoleon's friend the Italian mathematician Lorenzo Mascheroni introduced the limitation of using only a compass (no straight edge) into geometric constructions. But actually, the challenge above is easier than the real Napoleon's problem, consisting in finding the center of a given circle with compass alone. The following sections will describe solutions to both problems, and the proofs that they work.

In 1672, Georg Mohr produced a book, "Euclides Danicus", that predated Mascheroni, though the book was only rediscovered in 1928.