Visual Techniques For Computing Polyhedral Volumes

T. V. Raman
M. S. Krishnamoorthy


The volume of regular polyhedra have been a source of interest to geometers since the time of Plato and Aristotle, and formulae for computing the volumes of the dodecahedron and icosahedron can be traced back to ancient Greece. In this paper, we revisit these volumes from a slightly different perspective -we illustrate various constructions that permit the final formulae to be derived by simple visual inspection.

In presenting these techniques, we gain a fresh perspective on the relationship between the dodecahedron, icosahedron, cube, and the golden ratio f. The visual nature of these computational techniques in combination with zome models make these proofs easily accessible.

This paper was authored and typeset using the rich suite of Open Source tools available on the Linux desktop. At a time when most of the attention around Open Source Software is focused on the operating system, we would like to draw readers' attention to the wonderful array of high-quality Open Source authoring and document preparation tools created over the last 25 years by the (La)TeX community. Figures in this paper were drawn using declarative authoring packages that enabled the first author to draw reliably without having to look at the final output. The high-level markup also makes this content long-lived.

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