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For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

An isoscelizer of an (interior) angle A in a triangle DeltaABC is a line through points I_(AB)I_(AC) where I_(AB) lies on AB and I_(AC) on AC such that DeltaAI_(AB)I_(AC) is ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

Two or more lines or line segments which are perpendicular are said to be orthogonal.

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 study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 Kirkman points. Each Steiner point ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.