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Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

If two curves phi and psi of multiplicities r_i!=0 and s_i!=0 have only ordinary points or ordinary singular points and cusps in common, then every curve which has at least ...

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

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

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.

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

The fundamental theorem(s) of calculus relate derivatives and integrals with one another. These relationships are both important theoretical achievements and pactical tools ...