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The closure theorem of Poncelet

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Si dà conto di uno studio effettuato congiuntamente con C. Kers, F. Oort e D. W. Raven sugli aspetti storici e matematici del teorema di chiusura di Poncelet.

Sono discusse le dimostrazioni di Griffiths (1976), Jacobi (1828) e dello stesso Poncelet (1822), e si riporta un nuovo risultato concernente una certa famiglia di curve dipendenti da un parametro.

Questa famiglia di curve scaturisce in modo naturale dagli argomenti usati da Poncelet nella dimostrazione originale ed offre un caso interessante di non-commutatività forte di dualizzare e specializzare.

Summary

A report on a joint study together with C. Kers, F. Oort and D. W. Raven on historical and mathematical aspects of Poncelet's closure theorem. Proofs of the theorem by Griffiths (1976), Jacobi (1828) and Poncelet himself (1822) are discussed and a new result is reported concerning a certain one-parameter family of curves. This family of curves arises naturally from arguments in Poncelet's original proof and it offers an interesting case of strong non-commutativity of dualizing and specializing.

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Bibliography

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  1. dell'Università di Utrecht (Olanda), Utrecht, The Netherlands

    H. J. M. Bos

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(Conferenza tenuta il 15 ottobre 1984)

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Bos, H.J.M. The closure theorem of Poncelet. Seminario Mat. e. Fis. di Milano 54, 145–158 (1985). https://doi.org/10.1007/BF02924855

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