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A two-dimensional planar closed surface L which has a mass M and a surface density sigma(x,y) (in units of mass per areas squared) such that M=int_Lsigma(x,y)dxdy. The center ...

The azimuthal coordinate on the surface of a sphere (theta in spherical coordinates) or on a spheroid (in prolate or oblate spheroidal coordinates). Longitude is defined such ...

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has f^'(x) = ...

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

A quartic surface which is the locus of zeros of the determinant of a symmetric 4×4 matrix of linear forms. A general symmetroid has 10 ordinary double points (Jessop 1916, ...

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

Let (x_0,y_0) be any point of a surface function z=f(x,y). Then the surface has a nonvertical tangent plane at (x_0,y_0) with equation ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...