Ring Torus


One of the three standard tori given by the parametric equations


with c>a. This is the torus which is generally meant when the term "torus" is used without qualification. The inversion of a ring torus is a ring cyclide if the inversion center does not lie on the torus and a parabolic ring cyclide if it does. The above left figure shows a ring torus, the middle a cutaway, and the right figure shows a cross section of the ring torus through the xz-plane.

See also

Cyclide, Horn Torus, Parabolic Ring Cyclide, Ring Cyclide, Spindle Torus, Standard Tori, Torus

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Gray, A. "Tori." §13.4 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 304-306, 1997.Pinkall, U. "Cyclides of Dupin." Ch. 3, §3 in Mathematical Models from the Collections of Universities and Museums: Commentary. (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 28-30, 1986.Pinkall, U. "Dupinsche Zykliden." Ch. 3, §3 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen: Kommentarband (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 30-33, 1986.

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Ring Torus

Cite this as:

Weisstein, Eric W. "Ring Torus." From MathWorld--A Wolfram Web Resource.

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