Archimedes' Spiral
An Archimedean Spiral with Polar equation
This spiral was studied by Conon, and later by Archimedes
in On Spirals about 225 BC. 
Archimedes was able to work out the lengths of various tangents to the spiral.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 curvecan be used as a cam to convert uniform circular motion into uniform linear motion. The cam consists of one arch of thespiral above the x-Axis together with its reflection in the x-Axis. Rotating this with uniformangular velocity 
about its center will result in uniform linear motion of the point whereit 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.
- Skewness
- Skew Polyomino
- Skew Quadrilateral
- Skew Symmetric Matrix
- Sklar's Theorem
- Skolem-Mahler-Lerch Theorem
- Skolem Paradox
- Skolem Sequence
- Slant Height
- Slice Knot
- Slide Move
- Slide Rule
- Slightly Defective Number
- Slightly Excessive Number
- Slip Knot
- Slope
- Slothouber-Graatsma Puzzle
- Slutzky-Yule Effect
- Sluze Pearls
- Smale-Hirsch Theorem
- Smale Horseshoe Map
- Small Cubicuboctahedron
- Small Ditrigonal Dodecacronic Hexecontahedron
- Small Ditrigonal Dodecicosidodecahedron
- Small Ditrigonal Icosidodecahedron