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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 ...

The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays O{ABCD} are connected by the ...

The number of empty neighbors of a cluster.

The number q in a star polygon {p/q}.

The product of any number of perspectivities.

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

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