Separations inside a cube
arXiv:math/0112296
Abstract
Two points are randomly selected inside a three-dimensional euclidian cube. The value l of their separation lies somewhere between zero and the length of a diagonal of the cube. The probability density P(l) of the separation is obtained analytically. Also a Monte Carlo computer simulation is performed, showing good agreement with the formulas obtained.
7 pages, 5 figures
References in corpus (12)
- Topology of the Universe: Theory and Observations
- Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes
- A Topological Signature in Cosmic Topology
- On Closed Einstein-de Sitter Universes
- Limits of crystallographic methods for detecting space topology
- Topological lens effects in universes with non-Euclidean compact spatial sections
- A New Crystallographic Method for Detecting Space Topology
- Cosmic Crystallography in Compact Hyperbolic Universes
- Cosmic crystallography: three multi-purpose functions
- Cosmic crystallography in a circle
- Cosmic crystallography: the hyperbolic isometries
- Distances in plane membranes