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Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

The converse of Pascal's theorem, which states that if the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie ...

The curve which is the envelope of reflected (catacaustic) or refracted (diacaustic) rays of a given curve for a light source at a given point (known as the radiant point).

A central angle is an angle ∠AOC with endpoints A and C located on a circle's circumference and vertex O located at the circle's center (Rhoad et al. 1984, p. 420). A central ...

The first type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. Christoffel symbols of the first kind are variously ...

A curve whose name means "shell form." Let C be a curve and O a fixed point. Let P and P^' be points on a line from O to C meeting it at Q, where P^'Q=QP=k, with k a given ...

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

Let Delta_1, Delta_2, and Delta_3 be tetrahedra in projective three-space P^3. Then the tetrahedra are said to be desmically related if there exist constants alpha, beta, and ...