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A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

The gamma product (e.g., Prudnikov et al. 1986, pp. 22 and 792), is defined by Gamma[a_1,...,a_m; b_1,...,b_n]=(Gamma(a_1)...Gamma(a_m))/(Gamma(b_1)...Gamma(b_n)), where ...

The great rhombicuboctahedron (Cundy and Rowlett 1989, p. 106) is the 26-faced Archimedean solid consisting of faces 12{4}+8{6}+6{8}. It is sometimes called the ...

The dual of the great truncated icosahedron U_(55) and Wenninger dual W_(95).

A half-plane is a planar region consisting of all points on one side of an infinite straight line, and no points on the other side. If the points on the line are included, ...

A pyramidal number of the form n(n+1)(4n-1)/6, The first few are 1, 7, 22, 50, 95, ... (OEIS A002412). The generating function of the hexagonal pyramidal numbers is ...