Saw this beautiful square and rectangle spiral by Charmion von Wiegand the other day (http://mathhombre.tumblr.com/post/158045008339/topcat77-the-american-charmion-von-wiegand) and wanted to explore the structure. It turns out to be a very specific rectangle, square and scale factor to get this exact structure. This sketch is set up so that when the rectangle is the right proportion, the scale factor will make the perfect spiral. If the rectangle has the proportions a x 1, then the scale factor is a lovely r = (1+sqrt(1+4a))/2
A perfect inward spiral is also possible! Having defined the scale factor as above, what proportion should the rectangle be?
