An Archimedean Spiral with Polar equation

This spiral was studied by Conon, and later by Archimedes in

Archimedes' spiral can be used for Compass and Straightedge division of an Angle into parts
(including Angle Trisection) and can also be used for Circle Squaring. In addition, the curve
can be used as a cam to convert uniform circular motion into uniform linear motion. The cam consists of one arch of the
spiral above the *x*-Axis together with its reflection in the *x*-Axis. Rotating this with uniform
angular velocity about its center will result in uniform linear motion of the point where
it crosses the *y*-Axis.

**References**

Gardner, M. *The Unexpected Hanging and Other Mathematical Diversions.* Chicago, IL: Chicago University Press,
pp. 106-107, 1991.

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 69-70, 1993.

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 186-187, 1972.

Lockwood, E. H. *A Book of Curves.* Cambridge, England: Cambridge University Press, pp. 173-164, 1967.

© 1996-9

1999-05-25