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Algebraic Surface


The set of roots of a polynomial f(x,y,z)=0. An algebraic surface is said to be of degree n=max(i+j+k), where n is the maximum sum of powers of all terms a_mx^(i_m)y^(j_m)z^(k_m). The following table lists the names of algebraic surfaces of a given degree.


See also

Barth Decic, Barth Sextic, Boy Surface, Cayley Cubic, Chair Surface, Chmutov Surface, Clebsch Diagonal Cubic, Cushion Surface, Dervish, Endraß Octic, Heart Surface, Henneberg's Minimal Surface, Kummer Surface, Labs Septic, Roman Surface, Sarti Dodecic, Surface, Togliatti Surface

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References

Banchoff, T. F. "Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order." In Geometric Analysis and Computer Graphics: Proceedings of a Workshop Held May 23-25, 1988 (Eds. P. Concus, R. Finn, D. A. Hoffman). New York: Springer-Verlag, pp. 31-37, 1991.Beutel, E. Algebraische Kurven. Leipzig, Germany: Teubner, 1909.Fischer, G. (Ed.). Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband. Braunschweig, Germany: Vieweg, p. 7, 1986.Hauser, H. "Gallery of Singular Algebraic Surfaces." https://homepage.univie.ac.at/herwig.hauser/gallery.html.

Referenced on Wolfram|Alpha

Algebraic Surface

Cite this as:

Weisstein, Eric W. "Algebraic Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicSurface.html

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