Serpentine Curve

A curve named and studied by Newton in 1701 and contained in his classification of L'Hospital and Huygens in 1692 (MacTutor Archive).

The curve is given by the Cartesian equation

(1)

			(2)
			(3)

The curve has a Maximum at and a Minimum at , where

(4)

(5)

			(6)
			(7)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 111-112, 1972.

MacTutor History of Mathematics Archive. ``Serpentine.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Serpentine.html.

• Cayleyian Curve
• Cayley-Klein-Hilbert Metric
• Cayley-Klein Parameters
• Cayley Number
• Cayley's Group Theorem
• Cayley's Hypergeometric Function Theorem
• Cayley's Ruled Surface
• Cayley's Sextic
• Cayley's Sextic Evolute
• Cayley Tree
• C-Curve
• C-Determinant
• Cech Cohomology
• Ceiling Function
• Cell
• Cellular Automaton
• Cellular Space
• Center
• Centered Cube Number
• Centered Hexagonal Number
• Centered Pentagonal Number
• Centered Polygonal Number
• Centered Square Number
• Centered Triangular Number
• Center Function