Napoleon's problem is a 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 three problems and proofs that they work. Georg Mohr's 1672 book "Euclides Danicus" anticipated Mascheroni's idea, though the book was only rediscovered in 1928. Dividing a given circle into four equal arcs given its centre Centred on any point X on circle C, draw an arc through O (the centre of C) which intersects C at points V and Y. Do the same centred on Y through O, intersecting C at X and Z. Note that the line segments OV, OX, OY, OZ, VX, XY, YZ have the same length, all distances being equal to the radius of the circle C. Now draw an arc centred on V which goes through Y and an arc centred on Z which goes through X; call where these two arcs intersect T. Note that the distances VY and XZ are times the radius of the circle C. Put the compass radius equal to the distance OT ( times the radius of the circle C) and draw an arc centred on Z which intersects the circle C at U and W. UVWZ is a square and the arcs of C UV, VW, WZ, and ZU are each equal to a quarter of the circumference of C. Finding the centre of a given circle Let (C) be the circle, whose centre is to be found. Let A be a point on (C). A circle (C1) centered at A meets (C) at B and B'. Two circles (C2) centered at B and B', with radius AB, cross again at point C. A circle (C3) centered at C with radius AC meets (C1) at D and D'. Two circles (C4) centered at D and D' with radius AD meet at A, and at O, the sought center of (C). Note: for this to