Search Results for ""

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

The von Staudt-Clausen theorem, sometimes also known as the Staudt-Clausen theorem (Carlitz 1968), states that B_(2n)=A_n-sum_(p_k; (p_k-1)|2n)1/(p_k), (1) where B_(2n) is a ...

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 ...

The Brinkmann graph (misspelled by Cancela et al. (2004) as "Brinkman") is a weakly regular quartic graph on 21 vertices and 42 edges. It was first mentioned in Brinkmann ...

An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. For ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...