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A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

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 ...

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

The tangential mid-arc circle is the circumcircle of the tangential mid-arc triangle. Its center and radius appear to be very complicated functions. Its center is not in ...

The dual polyhedron of the cubitruncated cuboctahedron U_(16) and Wenninger dual W_(79).

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

Coordinates useful for plotting projective three-dimensional curves of the form f(x_0,x_1,x_2,x_3)=0 which are defined by x_0 = 1-z-sqrt(2)x (1) x_1 = 1-z+sqrt(2)x (2) x_2 = ...

A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 20-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...