Heron's Formula in Higher Dimensions
Name
6_2023_Article_1305.pdf
Size
1.53 MB
Format
Adobe PDF
Checksum (MD5)
5e1dcb9a83d63290ed11111e1a5f3e3b
Author(s)
Havel, Timothy F.
Date Issued
February 2024
Journal
Advances in Applied Clifford Algebras
Citation
Havel, Timothy F. 2024. "Heron's Formula in Higher Dimensions." Advances in Applied Clifford Algebras, 34.
Version
Final published version
Abstract
This paper shows how geometric algebra can be used to derive a novel generalization of Heron’s classical formula for the area of a triangle in the plane to higher dimensions. It begins by illustrating some of the many ways in which the conformal model of three-dimensional Euclidean space yields provocative insights into some of our most basic intuitive notions of solid geometry. It then uses this conceptual framework to elucidate the geometric meaning of Heron’s formula in the plane, and explains in detail how it extends naturally to the volumes of tetrahedra in space. The paper closes by outlining a proof of a previously conjectured extension of the formula to the hyper-volumes of simplices in all dimensions.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
10.1007/s00006-023-01305-8
https://doi.org/10.1007/s00006-023-01305-8
