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A transformation consisting of rotations and translations which leaves a given arrangement unchanged.

A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result ...

The inversion of a ring torus. If the inversion center lies on the torus, then the ring cyclide degenerates to a parabolic ring cyclide.

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

A pseudocylindrical map projection which distorts shape, area, scale, and distance to create attractive average projection properties.

dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

|_n]={n for n!=0; 1 for n=0. (1)

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).