ScholarLens Back to search
2004•Journal of Interdisciplinary MathematicsRequires access

The probability that a random ball is contained in a given ball

Uwe Saint‐Mont

Open publisher page 0 citations

Abstract

Denote by Bn(R) a ball of radius R in n -dimensional space. Successively choose points C, A ∈ Bn(R) at random. Then the probability that the n -dimensional ball Bn(C, AC) , having center C and radius AC , is entirely contained in Bn(R) is n!n!=(2n)! . The result holds for every metric and . It can be generalized to n -dimensional cubes in n -dimensional cuboids.

About this research paper

What this paper is about

Denote by Bn(R) a ball of radius R in n -dimensional space. Successively choose points C, A ∈ Bn(R) at random. Then the probability that the n -dimensional ball Bn(C, AC) , having center C and radius AC , is entirely contained in Bn(R) is n!n!=(2n)! . The result holds for every metric and . It can be generalized to n -dimensional cubes in n -dimensional cuboids.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Denote by Bn(R) a ball of radius R in n -dimensional space. Successively choose points C, A ∈ Bn(R) at random. Then the probability that the n -dimensional ball Bn(C, AC) , having center C and radius AC , is entirely contained in Bn(R) is n!n!=(2n)! . The result holds for every metric and . It can be generalized to n -dimensional cubes in n -dimensional cuboids.

Key concepts: Ball (mathematics), Mathematics, Combinatorics, Metric space, Geometry, RADIUS, Mathematical analysis, Computer science

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The probability that a random ball is contained in a given ball — Research Paper | ScholarLens