The resistance of an n-dimensional tetrahedron

Abstract

We consider here a problem that is suitable for introducing high-school students to the notion of generalizing shapes and solids to n dimensions. In particular, we calculate the effective resistance between any two vertices of an n-dimensional tetrahedron whose edges are each 1-Ω resistors. This leads, in a natural way, to more demanding problems, and indeed ideas for more advanced work in this area are also suggested.

Keywords:

• graphs
• Kirchhoff's laws
• n dimensions
• resistance
• tetrahedron