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Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

The Galilean spiral is the curve with polar equation r=btheta^2-a for a>0 which describes the trajectory of a point uniformly accelerated along a line rotating about a point.

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 ...

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

Consider two closed oriented space curves f_1:C_1->R^3 and f_2:C_2->R^3, where C_1 and C_2 are distinct circles, f_1 and f_2 are differentiable C^1 functions, and f_1(C_1) ...

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.