Here
is the spreadsheet that started this. It calculates the geometry of "polygons" used in machinery to transmit torque. This example is for P3, or three lobe shape. It measures "round" with a micrometer, although it is obvously not. Check Stoffel Polygon Systems for more about using this type of connection.
polygon.xls (55 KB)
Here's the spreadsheet so you can make your own spirals. (Try some multiples of pi or irrational numbers like radical 2.)
spiro.xls (246 KB)
Here's another one:
A Different Spiral
And a few external links related to similar geometry that look very cool - I have not explored all of it.
Simulating Harmonographs
New Math Model Finds That The Cochlea's Spiral Shape Enhances Low Frequencies