Fred and Tex: After reading the exchange on here today, I went back and re-read Fred's Compendium article, looking closer at the development of the gnomon shape as a cycloid. Sketching the path of a point on a circle, rolling on a line, I see the gnomon's shape (convex away from the line) as the curve traced out between two cusps of the cycloid. Does this sound right?
Given an arbitrary wheel diameter, can we then divide the straight line equally into twelve periods, from cusp to cusp, and get the hour lines to match the gnomon? It's pretty clear that the noon lines and sunrise/sunset line are correct, but I'm not certain if the others "automatically" fall on the right points... Assuming the circle rotates at a constant rate, then do the hour lines correspond to the twelve points where 30 degree segments of the circle touch down on the generating line? Dave
