Normalsized hypercuboids in a given hypercube
Abstract
In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the volumes of those hypercuboids (or hypercubes) to the entire volume as the grid spacing becomes smaller.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.15342
 arXiv:
 arXiv:2211.15342
 Bibcode:
 2022arXiv221115342H
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory;
 11B65;
 28A75;
 33B15
 EPrint:
 3 pages