Generalizing the Equal Incircles Theorem: Insights from Sangaku Problems

Authors

  • Perawit Boonsomchua King Mongkut University of Technology Thonburi

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5300

Keywords:

Sangaku problems , Equal incircle theorem , Angela Drei’s proof

Abstract

Sangaku problems are traditional Japanese geometrical puzzles, often displayed in religious temples, that have intrigued mathematicians for centuries. This study aims to generalize the Equal Incircles Theorem, extending Angela Drei’s proof to N-circles, by applying the trigonometric method alongside foundational mathematical tools, including mathematical induction, Heron’s formula, and the telescoping product. A generalized equation for N circles based on the Equal Incircles Theorem is derived through explicit mathematical formulation and characterization. The findings deepen our understanding of geometric relationships, highlight the historical significance of Sangaku problems, and offer potential advancements for future engineering applications, mathematics education, and research in mathematical history.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Generalizing the Equal Incircles Theorem: Insights from Sangaku Problems. (2024). European Journal of Pure and Applied Mathematics, 17(4), 4135-4146. https://doi.org/10.29020/nybg.ejpam.v17i4.5300