Some Elementary Aspects of 4-Dimensional Geometry

Abstract

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.

Keywords

• Heron’s formula
• scissors congruence
• Nicomachus’s theorem
• hypercube
• four-dimensional geometry
• hyper-solids