## Quick Reference

A curve whose equation in polar coordinates is *r*=*ae*^{kθ}, where *a* (>0) and *k* are constants. Let *O* be the origin and *P* be any point on the curve. The curve derives its name from the property that the angle α between *OP* and the tangent at *P* is constant. In fact, *k*=cot α. The equation can be written *r*=*kθ*+b, and the curve is also called the logarithmic spiral.

http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/KURSATgeometrypro/related%20curves/related%20curves.html Animations of related curves, and an interactive manipulative of the spiral in Geometer's Sketchpad.

*Subjects:*
Mathematics.