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Solving the Fagnano’s Problem via a Dynamic Geometry Approach

  • Yiu-Kwong Man
Conference paper

Abstract

The Fagnano’s problem is a famous historical problem in plane geometry, which involves finding an inscribed triangle with minimal perimeter in a given acute triangle. We discuss how to solve this problem via a dynamic geometry approach and derive a simple formula for finding the perimeter of the orthic triangle, which is the solution of the Fagnano’s problem. Some illustrative examples are included.

Keywords

Billiard trajectory Dynamic geometry approach Fagnano’s problem GeoGebra Heron’s theorem Minimal perimeter Orthic triangle 

Notes

Acknowledgements

This article is a revised version of the paper presented orally by the author at the International Multi-Conference of Engineers and Computer Scientists (IMECS 2017) held on 15–17 March 2017 at Hong Kong [12].

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Information TechnologyThe Education University of Hong KongTai Po, New TerritoriesHong Kong

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