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The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

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 ...