Jakob Steiner's \textit{Systematische Entwickelung}: the culmination of classical geometry
type: Item
instance of: scholarly article
title: Jakob Steiner's \textit{Systematische Entwickelung}: the culmination of classical geometry
zbMATH Open document ID: 1157.51002
author: Viktor Blåsjö
published in: The Mathematical Intelligencer
publication date: 2009-02-11T00:00:00Z
review text: This is both a reasonably detailed presentation of the content and of the aims of Jakob Steiner's \textit{Systematische Entwickelung} of 1832, as well as a critique of the historiography devoted to 19th century projective geometry, which has systematically downplayed the significance of Steiner's work and favoured that of K. G. C. von Staudt. It is shown that Steiner marvelously succeeds in achieving his stated aim of a grand unification of the results of classical geometry under the aegis of projective geometry, of extracting ``a thread of continuity and a common root'' from classical geometry, but that historiographers, led by Felix Klein, ``imposed different standards of success, downplaying historical continuity and favouring intrinsically motivated programmatic agendas\dots in the case of projective geometry epitomised by von Staudt's \textit{Geometrie der Lage} (1847)''. It should be noted that, less than 70 years after Klein's disparaging views on Steiner and praise for von Staudt appeared in print, the heritage of both Steiner and von Staudt coexisted peacefully in Erlangen in [\textit{K. Strambach}, Arch. Math. 64, No.~2, 170--184 (1995; Zbl 0820.51002)], where it is shown that, in arbitrary projective planes, the largest class of conics is that of conics defined by Steiner. Klein had criticised Steiner for being too restrictive with what would count as a conic: ``though there are two conics \(x_1^2+x_2^2-x_3^2\) and \(x_1^2+x_2^2+x_3^2\) from a projective point of view, in Steiner's system there is no room for the second.''
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51-03
Mathematics Subject Classification ID: 51A30
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A85
zbMATH DE Number: 5506571
zbMATH Keywords: Jakob Steiner
zbMATH Keywords: K. G. C. von Staudt
zbMATH Keywords: projective geometry
describes a project that uses: AEGIS
MaRDI profile type: Publication
full work available at URL: s00283-008-9012-z
OpenAlex ID: W2006018784
cites work: The Isoperimetric Problem
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DOI: 10.1007/S00283-008-9012-Z
description: scientific article; zbMATH DE number 5506571