单词 | Cyclide |
释义 | Cyclide![]() ![]() ![]() A pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called aCyclid. The cyclide is a Quartic Surface, and the lines of curvature on a cyclide are all straight lines orcircular arcs (Pinkall 1986). The Standard Tori and their inversions in a Sphere ![]() are both cyclides (Pinkall 1986). Illustrated above are Ring Cyclides,Horn Cyclides, and Spindle Cyclides. The figures on theright correspond to ![]()
Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, p. 273, 1959. Eisenhart, L. P. ``Cyclides of Dupin.'' §133 in A Treatise on the Differential Geometry of Curves and Surfaces. New York: Dover, pp. 312-314, 1960. Fischer, G. (Ed.). Plates 71-77 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 66-72, 1986. Nordstrand, T. ``Dupin Cyclide.'' http://www.uib.no/people/nfytn/dupintxt.htm. Pinkall, U. ``Cyclides of Dupin.'' §3.3 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 28-30, 1986. Salmon, G. Analytic Geometry of Three Dimensions. New York: Chelsea, p. 527, 1979. |
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