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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.

Order Surface
3 Cubic Surface
4 Quartic Surface
5 Quintic Surface
6 Sextic Surface
7 Heptic Surface
8 Octic Surface
9 Nonic Surface
10 Decic Surface

See also Barth Decic, Barth Sextic, Boy Surface, Cayley Cubic, Chair, Clebsch Diagonal Cubic, Cushion, Dervish, Endraß Octic, Heart Surface, Kummer Surface, Order (Algebraic Surface), Roman Surface, Surface, Togliatti Surface


Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, p. 7, 1986.

© 1996-9 Eric W. Weisstein