Solving the Fagnano’s problem via a dynamic geometry approach

Research output: Chapter in Book/Report/Conference proceedingChapter

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. Copyright © 2018 Springer Nature Singapore Pte Ltd.
Original languageEnglish
Title of host publicationTransactions on engineering technologies: International MultiConference of Engineers and Computer Scientists 2017
EditorsSio-Iong AO, Haeng Kon KIM, Oscar CASTILLO, Alan Hoi-Shou CHAN, Hideki KATAGIRI
Place of PublicationSingapore
PublisherSpringer
Pages243-251
ISBN (Electronic)9789811074882
ISBN (Print)9789811074875
DOIs
Publication statusPublished - 2018

Citation

Man, Y.-K. (2018). Solving the Fagnano’s problem via a dynamic geometry approach. In S.-I. Ao, H. K. Kim, O. Castillo, A. H.-S. Chan, & H. Katagiri (Eds.), Transactions on engineering technologies: International MultiConference of Engineers and Computer Scientists 2017 (pp. 243-251). Singapore: Springer.

Keywords

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

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