L'ipocicloide tricuspide: Il duplice approccio di Luigi Cremona ed Eugenio Beltrami
01 Jan 2018-Bollettino Di Storia Delle Scienze Matematiche (Fabrizio Serra Editore)-Vol. 38, Iss: 1, pp 61-92
About: This article is published in Bollettino Di Storia Delle Scienze Matematiche.The article was published on 2018-01-01 and is currently open access. It has received 3 citations till now.
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TL;DR: In this article, the authors examine the evolution of a specific mathematical problem, i.e., the nine-point conic, a generalisation of the ninepoint circle due to Steiner, and follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini).
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TL;DR: In this paper, the authors examine the evolution of a specific mathematical problem, i.e., the nine-point conic, from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey.
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 ninepoint 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.
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01 Jan 2023
TL;DR: In this paper , the authors reconstructed the biographies, careers, studies, and relationships of the students of the Italian school of algebraic geometry from the letters from Eugenio Bertini, Ettore Caporali, and Riccardo De Paolis.
Abstract: Luigi Cremona is considered the founder of the Italian school of algebraic geometry. He formed a group of students of great value, very active in scientific research. Examining the letters from Eugenio Bertini, Ettore Caporali, and Riccardo De Paolis to Cremona preserved in the archive of the Istituto Mazziniano in Genoa, we have reconstructed their biographies, careers, studies, and relationships with their teacher. They had the merit of cultivating the scientific innovations of the period and passing them on to the subsequent generations.