Crockett Johnson, creator of the 1955 youngsters’s ebook Harold and the Purple Crayon, was educated as an engineer and produced greater than 100 work primarily based on diagrams used within the proofs of classical theorems. This one, Polar Line of a Level and a Circle (Apollonius), seems to have been impressed by a determine in Nathan A. Courtroom’s 1966 School Geometry. The 2 circles are orthogonal: They minimize each other at proper angles. And because the sq. of the road connecting their facilities equals the sum of the squares of their radii, these three segments type a proper triangle.
Johnson was impressed to this work by his admiration of classical Greek structure. Sitting in a restaurant in Syracuse in 1973, he managed to assemble a heptagon utilizing seven toothpicks and the sides of a menu and a wine checklist, a development that had eluded the Greeks. (He discovered later that Archibald Finlay had illustrated comparable constructions in 1959.)
(Stephanie Cawthorne and Judy Inexperienced, “Harold and the Purple Heptagon,” Math Horizons 17:1 , 5-9.)