Article ID Journal Published Year Pages File Type
1158531 Historia Mathematica 2011 8 Pages PDF
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.

RiassuntoIl teorema di confronto fra gli angoli di due triangoli geodetici con uguali lati descritti sopra superficie di curvature diverse, comunemente attribuito per il caso bidimensionale a A.D. Alexandrov (1948) e per il caso n-dimensionale riemanniano a V.A. Toponogov (1959), risale, per il caso bidimensionale, a Paolo Pizzetti (1907b). Oltre a proporre una correzione storica riguardante l’origine e i primi sviluppi della geometria di confronto, la presente nota indica anche alcuni possibili motivi per la predetta dimenticanza.

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Physical Sciences and Engineering Mathematics Mathematics (General)
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