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A Surface of Revolution with constant Nonzero Mean Curvature also called an Onduloid. It is a Roulette obtained from the path described by the Foci of a Conic Section when rolled on a Line. This curve then generates an unduloid when revolved about the Line. These curves are special cases of the shapes assumed by soap film spanning the gap between prescribed boundaries. The unduloid of a Parabola gives a Catenoid.
See also Calculus of Variations, Catenoid, Roulette
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 48, 1989.
Delaunay, C. ``Sur la surface de révolution dont la courbure moyenne est constante.'' J. math. pures appl. 6, 309-320, 1841.
do Carmo, M. P. ``The Onduloid.'' §3.5G in
Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer).
Braunschweig, Germany: Vieweg, pp. 47-48, 1986.
Fischer, G. (Ed.). Plate 97 in
Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume.
Braunschweig, Germany: Vieweg, p. 93, 1986.
Thompson, D'A. W. On Growth and Form, 2nd ed., compl. rev. ed.
New York: Cambridge University Press, 1992.
Yates, R. C. A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, p. 184, 1952.