Log Spiral Approximation
A classic method for making a logarithmic spiral is known at least as far back as Descartes. (He and Bernoulli called them miraculous spirals.) Divide up the 360 degrees around a central point with equally spaced arms. Pick a starting point on one arm, then construct edges from one arm to the next and repeat.
1) What's the rule for making an edge in this sketch?
2) Why would the ratios from edge to edge be the same?
3) Why do we call them logarithmic spirals now?
4) Would an other edge making rules result in a logarithmic spiral?