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The surface generated by a twisted curve C when rotated about a fixed axis A and, at the same time, displaced parallel to A so that the velocity of displacement is always ...

Let a spherical triangle Delta have angles A, B, and C. Then the spherical excess is given by Delta=A+B+C-pi.

The great inverted snub icosidodecahedron is the uniform polyhedron with Maeder index 69 (Maeder 1997), Wenninger index 113 (Wenninger 1989), Coxeter index 73 (Coxeter et al. ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines. The two ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

Let F(m,n) be the number of m×n (0,1)-matrices with no adjacent 1s (in either columns or rows). For n=1, 2, ..., F(n,n) is given by 2, 7, 63, 1234, ... (OEIS A006506). The ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an ...