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Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

An arbitrary rotation may be described by only three parameters.

The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.

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 ...

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.