Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler
type: Item
instance of: scholarly article
title: Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler
zbMATH Open document ID: 0879.01008
author: J. V. Field
published in: Archive for History of Exact Sciences
publication date: 1998-01-19T00:00:00Z
review text: ``Rediscovering the Archimedean Polyhedra'' suggests a process similar to the well-known recovery of the classical texts of Euclid, Apollonius, Archimedes and others. However, it is made clear by Dr. Field in the first paragraph that ``rediscovery'' here does not refer to a ``lost'' classical text but to the mathematics involved in the construction of these solids. The evidence that Archimedes had known these 13 solids, whose faces are regular polygons of more than one kind, lies in Pappus who listed them with some details of these faces. Elements, Books 14 and 15 (pseudo-Euclid) treat regular polyhedra but were not used as a source, with the possible exception of Piero Della Francesca. However, even this debt is somewhat doubtful. What is traced is a characteristically Renaissance contribution to mathematics, connected, sometimes tenuously, to the Classical past. As in other Renaissance developments, the Classical past turns out to be only a ``jumping-off'' ground and the mathematics which emerges, not surprisingly is marked by the characteristics of its own time and place. Dr. Field traces the work of `rediscovery' from Piero to Daniele Barbaro and refers briefly to Kepler's later rigorous mathematical treatment in Harmonices mundi libri V., Book 2, in which Kepler constructed the first known complete set of Archimedean solids and proved the completeness. The main content of the article is a meticulous examination of the first five authors named in the title; the methods, achievements and `shortcomings' of each; possible methods of discovery are speculated upon; methods of construction by truncation or by nets are clearly and concisely explained. A helpful table of solids is provided showing which authors are associated with each. The many illustrations are supplemented with the author's own explicatory diagrams. An Appendix on the differing conventions used in drawing the solids puts to rest what has been, for many, an over-simplified picture of perspective drawi…
reviewed by: Muriel Seltman
Mathematics Subject Classification ID: 01A40
zbMATH DE Number: 1047103
zbMATH Keywords: regular polyhedra
zbMATH Keywords: Leonardo da Vinci
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1047103