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A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and ...

The point-slope form of a line through the point (x_1,y_1) with slope m in the Cartesian plane is given by y-y_1=m(x-x_1).

The roulette of the pole of a hyperbolic spiral rolling on a straight line is a tractrix.

A line segment where two faces of a polyhedron meet, also called a side.

The slope b of a line obtained using linear least squares fitting is called the regression coefficient.

An n-route is defined as a walk of length n with specified initial point in which no line succeeds itself.

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

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 ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...