- John Golden
Two types of spirals here. One way to approximate a logarithmic spiral is with evenly space rays, having the almost curve turn at a right angle to each ray. (Here's a GeoGebra sketch of that idea: http://www.geogebratube.org/material/show/id/14470) This sketch is a generalization of that idea, allowing any angle between rays instead of just divisors of 360 degrees. The other way is a generalization of the ancient construction of Theodorus, who made a spiral by adjacent right triangles, the first with legs 1x1. This has the wonderful property of the second triangle being root 2 by 1, and then root 3, root 4, etc. See Jennifer Silverman's sketch comparing it to an large artwork: http://www.geogebratube.org/material/show/id/43788. This sketch generalizes it by allowing you to make the original triangle any proportions. Are the Theodorish Spirals approximations of log spirals? What do you think and why?
More GeoGebra at mathhombre.blogspot.com