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Some Elementary Aspects of 4-Dimensional Geometry

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA
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Academic Editor: Louis H. Kauffman
Symmetry 2015, 7(2), 515-545; https://doi.org/10.3390/sym7020515
Received: 3 April 2015 / Revised: 27 April 2015 / Accepted: 27 April 2015 / Published: 4 May 2015
(This article belongs to the Special Issue Diagrams, Topology, Categories and Logic)
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. View Full-Text
Keywords: Heron’s formula; scissors congruence; Nicomachus’s theorem; hypercube; four-dimensional geometry; hyper-solids Heron’s formula; scissors congruence; Nicomachus’s theorem; hypercube; four-dimensional geometry; hyper-solids
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MDPI and ACS Style

Carter, J.S.; Mullens, D.A. Some Elementary Aspects of 4-Dimensional Geometry. Symmetry 2015, 7, 515-545. https://doi.org/10.3390/sym7020515

AMA Style

Carter JS, Mullens DA. Some Elementary Aspects of 4-Dimensional Geometry. Symmetry. 2015; 7(2):515-545. https://doi.org/10.3390/sym7020515

Chicago/Turabian Style

Carter, J. S.; Mullens, David A. 2015. "Some Elementary Aspects of 4-Dimensional Geometry" Symmetry 7, no. 2: 515-545. https://doi.org/10.3390/sym7020515

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