In the early 1970s Crockett Johnson, author of the children’s book *Harold and the Purple Crayon*, sent a geometric diagram to a friend noting that the diagram “answers the question in so *many* minds ‘What do the straightedge lines and compass arcs do when two parabolas and a hyperbola double a cube, just stand watching?’” [Crockett Johnson to Mickey Rosenau, n.d., Rosenau Collection, Smithsonian Institution]. The diagram and the answer to this question are addressed at the end of this paper.