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The Hadwiger-Nelson problem asks for the chromatic number of the plane, i.e., the minimum number of colors needed to color the plane if no two points at unit distance one ...

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...

The distance a point moves due to shear divided by the perpendicular distance of a point from the invariant line.

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

The point that inversion of a curve is performed with respect to.

The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...