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The crossed trough is the surface z=x^2y^2. (1) The coefficients of its first fundamental form are E = 1+4x^2y^4 (2) F = 4x^3y^3 (3) G = 1+4x^4y^2 (4) and of the second ...

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...

A surface of revolution of the form r(phi)=a[1-esin^2phi-(3/8e^2+k)sin^2(2phi)], where k is a second-order correction to the figure of a rotating fluid.

The diameter of a circle is the distance from a point on the circle to a point pi radians away, and is the maximum distance from one point on a circle to another. The ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...

A point p on a regular surface M in R^3 is said to be elliptic if the Gaussian curvature K(p)>0 or equivalently, the principal curvatures kappa_1 and kappa_2 have the same ...

The group of rotations and translations.