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Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...

If three skew lines all meet three other skew lines, any transversal to the first set of three meets any transversal to the second set of three.

An arrangement of points with no three collinear, or of lines with no three concurrent.

In one dimension, the interval [0,1] is the closed unit interval, the interval (0,1) is the open unit interval, and the intervals (0,1] and [0,1) are half-open unit intervals.

A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

Two lines that lie on top of one another are called coincident lines.

A point, such as interior points of a disk, such that (px)(py)=[const], where p is the chord length.

Two objects which touch each other are said to be incident.

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

The locus of lines meeting three given skew lines. ("Regulus" is also the name of the brightest star in the constellation Leo.)