Cogliati, Alberto (Author)
Carocci Editore
Physical Details: 224 pp.
Language: Italian
La scoperta, o l’invenzione, della geometria non euclidea costituisce uno snodo fondamentale dello sviluppo storico della matematica; è difficile pensare a un evento che abbia avuto un impatto altrettanto diffuso e profondo. L’imporsi di una geometria alternativa a quella euclidea, infatti, non solo determinò mutamenti radicali nella concezione degli enti e degli assiomi della matematica, ma produsse effetti significativi e duraturi anche nel campo della logica, dei rapporti tra matematica e fisica e, più in generale, nell’ambito della teoria della conoscenza. Il volume propone una storia della geometria non euclidea ricostruendo, attraverso una trattazione rigorosa sia sul piano storico sia su quello matematico, il plurimillenario processo di riflessione sui fondamenti della disciplina che condusse, nella prima metà dell’Ottocento, matematici quali Bolyai, Gauss e Lobacevskij alla scoperta della geometria iperbolica. [Abstract translated by Google Translate: This is the abstract in English… The discovery, or invention, of non-Euclidean geometry constitutes a fundamental turning point in the historical development of mathematics; it is difficult to think of an event that has had such a widespread and profound impact. The imposition of an alternative geometry to the Euclidean one, in fact, not only brought about radical changes in the conception of the entities and axioms of mathematics, but also produced significant and lasting effects in the field of logic, of the relationships between mathematics and physics and, more specifically general, within the theory of knowledge. The volume proposes a history of non-Euclidean geometry by reconstructing, through a rigorous treatment on both a historical and mathematical level, the thousand-year-old process of reflection on the foundations of the discipline which led, in the first half of the nineteenth century, mathematicians such as Bolyai, Gauss and Lobacevskij discovering hyperbolic geometry.]
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