This snapshot explores Ptolemy's theorem's relevance in understanding surface shapes, suggesting its continued importance.
Ptolemy's theorem is a classical result from ancient Greek mathematics, concerning the lengths of sides and diagonals of a polygon drawn in a circle. In this snapshot, I will explain why this theorem is still important today through its role in Teichmüller theory, a subject which seeks to describe all possible ''shapes'' of a surface with boundary.
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Matthew Pressland (2026) studied this question.
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