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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 ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

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 ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

The Borromean rings, also called the Borromean links (Livingston 1993, p. 10) are three mutually interlocked rings (left figure), named after the Italian Renaissance family ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...