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...

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Bibliographic Details
Published in:Symmetry (Basel) 2015-06, Vol.7 (2), p.515-545
Main Authors: Carter, J Scott, Mullens, David A
Format: Article
Language:English
Subjects:
Congruences
Cutting tools
Decomposition
four-dimensional geometry
Heron’s formula
hyper-solids
hypercube
Hypercubes
Nicomachus’s theorem
scissors congruence
Symmetry
Triangles
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym7020515