An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. 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.
Unduloid
See also
Calculus of Variations, Catenoid, Roulette, Surface of RevolutionExplore with Wolfram|Alpha
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 aus den Sammlungen von Universitäten und Museen, Bildband. 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.Referenced on Wolfram|Alpha
UnduloidCite this as:
Weisstein, Eric W. "Unduloid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Unduloid.html