In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadratic transformations. In this sense, the work of Beltrami appears similar to the recent (after the anticipations of Magnus and Steiner) results of Schiaparelli and Cremona. Moreover, Beltrami's methods are closely related to the study of birational transformations, which in the same period were becoming one of the main topics of algebraic geometry. Finally, our work emphasises the role played by the nine-point conic problem in the studies of young Beltrami who, under Cremona's guidance, was then developing his mathematical skills. To this end, we make considerable use of the unedited correspondence Beltrami – Cremona, preserved in the Istituto Mazziniano, Genoa.

Vaccaro M.A. (2020). Historical origins of the nine-point conic. The contribution of Eugenio Beltrami. HISTORIA MATHEMATICA, 51, 26-48 [10.1016/j.hm.2019.12.002].

Historical origins of the nine-point conic. The contribution of Eugenio Beltrami

Vaccaro M. A.
2020-01-01

Abstract

In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadratic transformations. In this sense, the work of Beltrami appears similar to the recent (after the anticipations of Magnus and Steiner) results of Schiaparelli and Cremona. Moreover, Beltrami's methods are closely related to the study of birational transformations, which in the same period were becoming one of the main topics of algebraic geometry. Finally, our work emphasises the role played by the nine-point conic problem in the studies of young Beltrami who, under Cremona's guidance, was then developing his mathematical skills. To this end, we make considerable use of the unedited correspondence Beltrami – Cremona, preserved in the Istituto Mazziniano, Genoa.
Settore MAT/04 - Matematiche Complementari
Vaccaro M.A. (2020). Historical origins of the nine-point conic. The contribution of Eugenio Beltrami. HISTORIA MATHEMATICA, 51, 26-48 [10.1016/j.hm.2019.12.002].
File in questo prodotto:
File Dimensione Formato  
HM_Finale.pdf

Solo gestori archvio

Descrizione: articolo principale
Tipologia: Versione Editoriale
Dimensione 2.28 MB
Formato Adobe PDF
2.28 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
391693_Vaccaro.pdf

Open Access dal 01/01/2022

Tipologia: Post-print
Dimensione 1.23 MB
Formato Adobe PDF
1.23 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/391693
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact