Although Euclid solves more than 100 construction problems in the Elements, many more were posed whose solutions required more than just compass and straightedge. Three such problems stimulated so much interest among later geometers that they have come to be known as the “classical problems”: doubling the cube (i.e., constructing a cube whose volume is twice that of a given cube), trisecting the angle, and squaring the circle. Even in the pre-Euclidean period the effort to construct a square equal in area to a given circle had begun. Some related results came from Hippocrates (see Sidebar: Quadrature of the Lune); ...(100 of 41449 words)