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The product of three translations along the directed sides of a triangle through twice the lengths of these sides is the identity map.

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

The angle of incidence of a ray to a surface is measured as the difference in angle between the ray and the normal vector of the surface at the point of intersection.

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

The comass of a differential p-form phi is the largest value of phi on a p vector of p-volume one, sup_(v in ^ ^pTM,|v|=1)|phi(v)|.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

One of the "knots" t_(p+1), ..., t_(m-p-1) of a B-spline with control points P_0, ..., P_n and knot vector T={t_0,t_1,...,t_m}, where p=m-n-1.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.