On 8/16/2012 4:52 PM, Bill Gosper wrote:
Here's a piecewise linear spiral approximation to a nautilus (shown me by Jack Holloway): http://www.amazon.com/The-Irrationals-Story-Numbers-Count/dp/0691143420/ref=...
Hi Bill, That's a "Spiral of Theodorus", which closely approximates an Archimedean spiral, not an exponential spiral. See: http://en.wikipedia.org/wiki/Spiral_of_Theodorus If the image on that book cover included another revolution, it would become obvious how it doesn't match the nautilus it is superimposed on. A nautilus grows by a multiplicative factor of roughly three each revolution, while the square root spiral grows by roughly an additive increment of Pi each revolution. It is very misleading for them to show just one revolution, so it looks like a reasonable model, but I don't think this error is commonly made. Do you know other places where the Spiral of Theodorus is used as a model of the nautilus? George http://georgehart.com/