Some Elementary Aspects of 4-Dimensional Geometry

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...

Full description

Bibliographic Details
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
Description
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

Similar Items