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) |
, where | (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.
- Archimedes' Lemma
- Archimedes' Midpoint Theorem
- Archimedes' Postulate
- Archimedes' Problem
- Archimedes' Recurrence Formula
- Archimedes' Spiral
- Archimedes' Spiral Inverse
- Arc Length
- Arc Minute
- Arcsecant
- Arc Second
- Arcsine
- Arctangent
- Area
- Area Element
- Areal Coordinates
- Area-Preserving Map
- Area Principle
- Arf Invariant
- Argand Diagram
- Argand Plane
- Argoh's Conjecture
- Argument Addition Relation
- Argument (Complex Number)
- Argument (Elliptic Integral)