A dynamic geometry approach to the Fagnano's problem

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The Fagnano's problem is a famous optimization problem in plane geometry, whose solution is given by the inscribed orthic triangle of a given acute triangle. In this paper, we discuss how to solve this problem by the principle of reflection via a dynamic geometry approach. Compared with the method of solutions based on Calculus or Euclidean Geometry only, this approach can be easily adapted to study similar problems in other settings. We will also introduce a useful formula for finding the perimeter of the orthic triangle. Copyright © 2017 International Association of Engineers.
Original languageEnglish
Title of host publicationProceedings of the International MultiConference of Engineers and Computer Scientists 2017 Vol I
EditorsS. I. AO, Oscar CASTILLO, Craig DOUGLAS, David Dagan FENG, A. M. KORSUNSKY
PublisherNewswood Limited
Pages117-120
ISBN (Print)9789881404732
Publication statusPublished - 2017

Citation

Man, Y.-K. (2017). A dynamic geometry approach to the Fagnano's problem. In S. I. Ao, O. Castillo, C. Douglas, D. D. Feng, & A. M. Korsunsky (Eds.), Proceedings of the International MultiConference of Engineers and Computer Scientists 2017 Vol I (pp. 117-120). Hong Kong: Newswood Limited.

Keywords

  • Fagnano problem
  • Minimal perimeter
  • Orthic triangle
  • Periodic billiard path
  • Dynamic geometry

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