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 language | English |
|---|---|
| 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 |
| Publisher | Springer |
| Pages | 243-251 |
| ISBN (Electronic) | 9789811074882 |
| ISBN (Print) | 9789811074875 |
| DOIs | |
| Publication status | Published - 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