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Pentagramma Mirificum and Elliptic Functions

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Vadim Schechtman
Université Paul Sabatier
Mon, 18/07/2011 - 14:00 - 15:00
MPIM Lecture Hall

In this talk I shall give an exposition of fragments from Gauss
where he discovered,
with the help of some work of Jacobi,
a remarkable connection between Napier pentagons on the sphere and Poncelet
pentagons on the plane.

This gives rise to a parametrization of the variety of Napier pentagons
the division by 5 of elliptic functions.

As a corollary we will find the classical five-term relation for the
dilogarithm in a somewhat
exotic disguise, and discuss some open questions.


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