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A path, also known as a rhumb line, which cuts a meridian on a given surface at any constant angle but a right angle. If the surface is a sphere, the loxodrome is a spherical ...

At the points where a line X cuts the sides of a triangle DeltaA_1A_2A_3, draw three perpendiculars to the sides, one through each point of intersection. The resulting three ...

Two triangles DeltaABC and DeltaA^'B^'C^' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet ...

Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...

A transformation of the plane which transforms collinear points into collinear points. A projective collineation transforms every one-dimensional form projectively, and a ...

Let P=p:q:r and U=u:v:w be distinct points, neither lying on a side line of the reference triangle DeltaABC. Then the P-cross conjugate of U is the point ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

Homogeneous coordinates (x_1,x_2,x_3) of a finite point (x,y) in the plane are any three numbers for which (x_1)/(x_3)=x (1) (x_2)/(x_3)=y. (2) Coordinates (x_1,x_2,0) for ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...