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In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

Barycentric coordinates are triples of numbers (t_1,t_2,t_3) corresponding to masses placed at the vertices of a reference triangle DeltaA_1A_2A_3. These masses then ...

When the index nu is real, the functions J_nu(z), J_nu^'(z), Y_nu(z), and Y_nu^'(z) each have an infinite number of real zeros, all of which are simple with the possible ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

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. ...

The Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...