Paolo Pizzetti: The forgotten originator of triangle comparison geometry

Victor Pambuccian, Tudor Zamfirescu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The theorem comparing the angles of two geodesic triangles with the same side lengths lying on surfaces with different curvatures, commonly attributed for the two-dimensional case to A.D. Alexandrov (1948) and for the n-dimensional Riemannian case to V.A. Toponogov (1959), goes back, for the two-dimensional case, to Paolo Pizzetti (1907b). Besides suggesting a correction of the historical narrative regarding the development of comparison geometry, the present note also mentions possible reasons for the oversight.

Original languageEnglish (US)
Pages (from-to)415-422
Number of pages8
JournalHistoria Mathematica
Volume38
Issue number3
DOIs
StatePublished - Aug 2011

Fingerprint

Triangle
Geodesic
n-dimensional
Curvature
Angle
Theorem
Historical Narrative
Geometry
Length
Narrative

Keywords

  • A.D. Alexandrov
  • Comparison geometry
  • Paolo Pizzetti
  • V.A. Toponogov

ASJC Scopus subject areas

  • History
  • Mathematics(all)

Cite this

Paolo Pizzetti : The forgotten originator of triangle comparison geometry. / Pambuccian, Victor; Zamfirescu, Tudor.

In: Historia Mathematica, Vol. 38, No. 3, 08.2011, p. 415-422.

Research output: Contribution to journalArticle

@article{990341b2ba1348bfa95278f99b0e719a,
title = "Paolo Pizzetti: The forgotten originator of triangle comparison geometry",
abstract = "The theorem comparing the angles of two geodesic triangles with the same side lengths lying on surfaces with different curvatures, commonly attributed for the two-dimensional case to A.D. Alexandrov (1948) and for the n-dimensional Riemannian case to V.A. Toponogov (1959), goes back, for the two-dimensional case, to Paolo Pizzetti (1907b). Besides suggesting a correction of the historical narrative regarding the development of comparison geometry, the present note also mentions possible reasons for the oversight.",
keywords = "A.D. Alexandrov, Comparison geometry, Paolo Pizzetti, V.A. Toponogov",
author = "Victor Pambuccian and Tudor Zamfirescu",
year = "2011",
month = "8",
doi = "10.1016/j.hm.2010.11.001",
language = "English (US)",
volume = "38",
pages = "415--422",
journal = "Historia Mathematica",
issn = "0315-0860",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - Paolo Pizzetti

T2 - The forgotten originator of triangle comparison geometry

AU - Pambuccian, Victor

AU - Zamfirescu, Tudor

PY - 2011/8

Y1 - 2011/8

N2 - The theorem comparing the angles of two geodesic triangles with the same side lengths lying on surfaces with different curvatures, commonly attributed for the two-dimensional case to A.D. Alexandrov (1948) and for the n-dimensional Riemannian case to V.A. Toponogov (1959), goes back, for the two-dimensional case, to Paolo Pizzetti (1907b). Besides suggesting a correction of the historical narrative regarding the development of comparison geometry, the present note also mentions possible reasons for the oversight.

AB - The theorem comparing the angles of two geodesic triangles with the same side lengths lying on surfaces with different curvatures, commonly attributed for the two-dimensional case to A.D. Alexandrov (1948) and for the n-dimensional Riemannian case to V.A. Toponogov (1959), goes back, for the two-dimensional case, to Paolo Pizzetti (1907b). Besides suggesting a correction of the historical narrative regarding the development of comparison geometry, the present note also mentions possible reasons for the oversight.

KW - A.D. Alexandrov

KW - Comparison geometry

KW - Paolo Pizzetti

KW - V.A. Toponogov

UR - http://www.scopus.com/inward/record.url?scp=79958047579&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958047579&partnerID=8YFLogxK

U2 - 10.1016/j.hm.2010.11.001

DO - 10.1016/j.hm.2010.11.001

M3 - Article

AN - SCOPUS:79958047579

VL - 38

SP - 415

EP - 422

JO - Historia Mathematica

JF - Historia Mathematica

SN - 0315-0860

IS - 3

ER -