Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)

Vadim Schechtman[1]

  • [1] Institut des Mathématiques de Toulouse, UPS, 118 route de Narbonne, 31062 Toulouse, France

Annales de la faculté des sciences de Toulouse Mathématiques (2013)

  • Volume: 22, Issue: 2, page 353-375
  • ISSN: 0240-2963

Abstract

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We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.

How to cite

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Schechtman, Vadim. "Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)." Annales de la faculté des sciences de Toulouse Mathématiques 22.2 (2013): 353-375. <http://eudml.org/doc/275393>.

@article{Schechtman2013,
abstract = {We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.},
affiliation = {Institut des Mathématiques de Toulouse, UPS, 118 route de Narbonne, 31062 Toulouse, France},
author = {Schechtman, Vadim},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {6},
number = {2},
pages = {353-375},
publisher = {Université Paul Sabatier, Toulouse},
title = {Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)},
url = {http://eudml.org/doc/275393},
volume = {22},
year = {2013},
}

TY - JOUR
AU - Schechtman, Vadim
TI - Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 2
SP - 353
EP - 375
AB - We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.
LA - eng
UR - http://eudml.org/doc/275393
ER -

References

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