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.
|Title of host publication||Transactions on engineering technologies: International MultiConference of Engineers and Computer Scientists 2017|
|Editors||Sio-Iong AO, Haeng Kon KIM, Oscar CASTILLO, Alan Hoi-Shou CHAN, Hideki KATAGIRI|
|Place of Publication||Singapore|
|Publication status||Published - 2018|
CitationMan, 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.
- Billiard trajectory
- Dynamic geometry approach
- Fagnano’s problem
- Heron’s theorem
- Minimal perimeter
- Orthic triangle