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 
centered at a point
and of Radius 
, given by
are both cyclides (Pinkall 1986). Illustrated above are Ring Cyclides,Horn Cyclides, and Spindle Cyclides. The figures on theright correspond to
lying on the torus itself, and are called the Parabolic Ring Cyclide,Parabolic Horn Cyclide, and Parabolic Spindle Cyclide, respectively.See also Cyclidic Coordinates, Horn Cyclide, Parabolic Horn Cyclide,Parabolic Ring Cyclide, Ring Cyclide, Spindle Cyclide, Standard Tori
References
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.
- Value
- Value (Game)
- Vampire Number
- van der Grinten Projection
- Vandermonde Determinant
- Vandermonde Identity
- Vandermonde Matrix
- Vandermonde's Sum
- Vandermonde Theorem
- van der Pol Equation
- van der Waerden Number
- van der Waerden's Theorem
- Vandiver's Criteria
- Vanishing Point
- van Kampen's Theorem
- van Wijngaarden-Deker-Brent Method
- Varga's Constant
- Variance
- Difference of Successes
- Difference Operator
- Difference Quotient
- Difference Set
- Difference Table
- Different
- Differentiable