English

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.

Keywords

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

R2 v1 2026-06-22T09:12:00.574Z