PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
March 4, 20260 citationsOpen Access

Triangulations in Geometry: from Ptolemy to Teichmüller

MPMatthew Pressland

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.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Matthew Pressland (2026) studied this question.

synapsesocial.com/papers/69a7cdf0d48f933b5eeda55dhttps://doi.org/10.14760/snap-2026-004-en
Ask AI
Helpful
Bookmark
Share
View Full Paper