Some Elementary Aspects of 4-Dimensional Geometry

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 four-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-para...

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Main Authors:	J. Scott Carter, David A. Mullens
Format:	Article
Language:	English
Published:	MDPI AG 2015-05-01
Series:	Symmetry
Subjects:	Heron’s formula scissors congruence Nicomachus’s theorem hypercube four-dimensional geometry hyper-solids
Online Access:	http://www.mdpi.com/2073-8994/7/2/515

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spelling	doaj-cff2fc5f9246440db85067f4583e54312020-11-24T23:54:03ZengMDPI AGSymmetry2073-89942015-05-017251554510.3390/sym7020515sym7020515Some Elementary Aspects of 4-Dimensional GeometryJ. Scott Carter0David A. Mullens1Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USADepartment of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USAWe 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 four-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms and other elementary four-dimensional solids.http://www.mdpi.com/2073-8994/7/2/515Heron’s formulascissors congruenceNicomachus’s theoremhypercubefour-dimensional geometryhyper-solids
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	J. Scott Carter David A. Mullens
spellingShingle	J. Scott Carter David A. Mullens Some Elementary Aspects of 4-Dimensional Geometry Symmetry Heron’s formula scissors congruence Nicomachus’s theorem hypercube four-dimensional geometry hyper-solids
author_facet	J. Scott Carter David A. Mullens
author_sort	J. Scott Carter
title	Some Elementary Aspects of 4-Dimensional Geometry
title_short	Some Elementary Aspects of 4-Dimensional Geometry
title_full	Some Elementary Aspects of 4-Dimensional Geometry
title_fullStr	Some Elementary Aspects of 4-Dimensional Geometry
title_full_unstemmed	Some Elementary Aspects of 4-Dimensional Geometry
title_sort	some elementary aspects of 4-dimensional geometry
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2015-05-01
description	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 four-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms and other elementary four-dimensional solids.
topic	Heron’s formula scissors congruence Nicomachus’s theorem hypercube four-dimensional geometry hyper-solids
url	http://www.mdpi.com/2073-8994/7/2/515
work_keys_str_mv	AT jscottcarter someelementaryaspectsof4dimensionalgeometry AT davidamullens someelementaryaspectsof4dimensionalgeometry
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Some Elementary Aspects of 4-Dimensional Geometry

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