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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 ...

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

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

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.

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

The gabled rhombohedra are a family of elongated gyrobifastigium that are space-filling. The equilateral elongated gyrobifastigium, illustrated above, is one such example.

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.

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...