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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 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

Regge calculus is a finite element method utilized in numerical relativity in attempts of describing spacetimes with few or no symmetries by way of producing numerical ...

The Danzer graph is the Levi graph of the Danzer configuration (Boben et al. 2015). It has 70 vertices and 140 edges and is quartic, bipartite, self-dual, and unit-distance. ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

The Gauss-Seidel method (called Seidel's method by Jeffreys and Jeffreys 1988, p. 305) is a technique for solving the n equations of the linear system of equations Ax=b one ...

The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p. 892). Each diagonal ...