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The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

There are two different definitions of "polar vector." In elementary math, the term "polar vector" is used to refer to a representation of a vector as a vector magnitude ...

A RAT-free ("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-free subset of ...

The regular nonagon is the regular polygon with nine sides and Schläfli symbol {9}. The regular nonagon cannot be constructed using the classical Greek rules of geometric ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...