Paolo Pizzetti: the forgotten originator of triangle comparison geometry
type: Item
instance of: scholarly article
title: Paolo Pizzetti: the forgotten originator of triangle comparison geometry
zbMATH Open document ID: 1221.01083
author: Victor V. Pambuccian
author: Tudor Zamfirescu
published in: Historia Mathematica
publication date: 2011-07-19T00:00:00Z
review text: The authors discuss forgotten contributions of Italian mathematician Paolo Pizzetti to the development of comparison geometry. In 1907, Pizzetti considered the two-dimensional case of the theorem comparing angles of two geodesic triangles with the same lengths lying on surfaces with different curvatures. Known authoritative historical sources provide very brief accounts of the origins and development of comparison geometry relating the theorem to the names of A. D. Alexandrov (1948) in the two-dimensional case and V. A. Toponogov (1959) in the \(n\)-dimensional Riemannian case. The authors argue that ``the proofs of Pizzetti and of Alexandrov and Toponogov cannot be meaningfully compared, given that, although the theorems are phrased similarly, the definitions of the terms involved are so different that the proofs could not have displayed any similarity'', yet Pizzetti's contributions to comparison geometry cannot be neglected. In addition to a brief biographical sketch, a short outline of Pizzetti's proof of the triangle comparison theorem is provided along with possible reasons for oblivion.
reviewed by: Svitlana P. Rogovchenko
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 5925778
zbMATH Keywords: comparison geometry
zbMATH Keywords: triangle comparison theorem
zbMATH Keywords: Paolo Pizzetti
zbMATH Keywords: A. D. Alexandrov
zbMATH Keywords: V. A. Toponogov
MaRDI profile type: Publication
full work available at URL: j.hm.2010.11.001
OpenAlex ID: W2026219188
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DOI: 10.1016/J.HM.2010.11.001
description: scientific article; zbMATH DE number 5925778