Roulette

The curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. Theroulettes described by the Foci of Conics when rolled upon a line are sectionsof Minimal Surfaces (i.e., they yield Minimal Surfaces when revolved about the line)known as Unduloids.

References

Besant, W. H. Notes on Roulettes and Glissettes, 2nd enl. ed. Cambridge, England: Deighton, Bell & Co., 1890.

Cundy, H. and Rollett, A. ``Roulettes and Involutes.'' §2.6 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 46-55, 1989.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 56-58 and 206, 1972.

Lockwood, E. H. ``Roulettes.'' Ch. 17 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 138-151, 1967.

Yates, R. C. ``Roulettes.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 175-185, 1952.

Zwillinger, D. (Ed.). ``Roulettes (Spirograph Curves).'' §8.2 in CRC Standard Mathematical Tables and Formulae, 3rd ed. Boca Raton, FL: CRC Press, 1996. http://www.geom.umn.edu/docs/reference/CRC-formulas/node34.html.

• Halphen's Transformation
• Halting Problem
• Hamiltonian Circuit
• Hamiltonian Cycle
• Hamiltonian Graph
• Hamiltonian Group
• Hamiltonian Map
• Hamiltonian Path
• Hamiltonian System
• Hamilton's Equations
• Hamilton's Rules
• Hammer-Aitoff Equal-Area Projection
• Hamming Function
• Ham Sandwich Theorem
• Handedness
• Handkerchief Surface
• Handle
• Handlebody
• Hankel Function
• Hankel Function of the First Kind
• Hankel Function of the Second Kind
• Hankel Matrix
• Hankel's Integral
• Hankel Transform
• Hann Function