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If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

If the three straight lines joining the corresponding vertices of two triangles ABC and A^'B^'C^' all meet in a point (the perspector), then the three intersections of pairs ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

The Brocard axis is the line KO passing through the symmedian point K and circumcenter O of a triangle, where the segment OK is the Brocard diameter (Kimberling 1998, p. ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

In general, a cross is a figure formed by two intersecting line segments. In linear algebra, a cross is defined as a set of n mutually perpendicular pairs of vectors of equal ...

The Burridge-Knopoff model is a system of differential equations used to model earthquakes using n points on a straight line, each of mass m, that interact with each other ...

A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...