Some Elementary Aspects of 4-dimensional Geometry
History and Overview
2015-04-09 v1 Metric Geometry
Abstract
We indicate that Heron's formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in 4-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms, and other elementary 4-dimensional solids.
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Cite
@article{arxiv.1504.01727,
title = {Some Elementary Aspects of 4-dimensional Geometry},
author = {J. Scott Carter and David A. Mullens},
journal= {arXiv preprint arXiv:1504.01727},
year = {2015}
}
Comments
35 pages; 34 full color figures