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The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

A geometric figure which touches only the sides (or interior) of another figure.

Two or more lines or line segments which are perpendicular are said to be orthogonal.

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

A plane figure for which quadrature is possible is said to be quadrable.

An object which can be constructed by squaring is called squarable.

A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.

If s_x is the standard deviation of a set of samples x_i and x^_ their mean, then the variation coefficient is defined as V=(s_x)/(x^_).

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

A bra <psi| is a vector living in a dual vector space to that containing kets |psi>. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be ...