What does this research mean for the field?

Ptolemy's theorem remains significant in contemporary mathematics due to its application in Teichmüller theory, which describes the shapes of surfaces with boundaries. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This work aims to illustrate the enduring relevance of Ptolemy's theorem in modern mathematics, particularly in Teichmüller theory.

March 4, 2026Open Access

Triangulations in Geometry: from Ptolemy to Teichmüller

Key Points

This work aims to illustrate the enduring relevance of Ptolemy's theorem in modern mathematics, particularly in Teichmüller theory.
Reviewing historical concepts of Ptolemy's theorem.
Explaining connections to Teichmüller theory.
Discussing geometrical implications of the theorem.
Ptolemy's theorem provides insight into the geometric properties of polygons.
Its applications are vital in the study of surface shapes in modern mathematics.

Abstract

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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Cite This Study

Matthew Pressland (Thu,) studied this question.

synapsesocial.com/papers/69a7cdf0d48f933b5eeda55d https://doi.org/https://doi.org/10.14760/snap-2026-004-en

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