Snell meets Fagnano. Path optimization through an imperfect mirror
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912742343966720 |
|---|---|
| author | Arnold, Maxim Park, Jaewoo |
| author_facet | Arnold, Maxim Park, Jaewoo |
| contents | The renowned Fagnano problem asks for the inscribed triangle of minimal perimeter within a given reference triangle. Equivalently, it seeks a billiard trajectory inside the triangle that closes after three reflections. In this note, we consider a modification of this classical problem: finding the inscribed triangle of minimal weighted perimeter -- or, equivalently, the periodic trajectory of a Snell billiard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Snell meets Fagnano. Path optimization through an imperfect mirror Arnold, Maxim Park, Jaewoo Dynamical Systems The renowned Fagnano problem asks for the inscribed triangle of minimal perimeter within a given reference triangle. Equivalently, it seeks a billiard trajectory inside the triangle that closes after three reflections. In this note, we consider a modification of this classical problem: finding the inscribed triangle of minimal weighted perimeter -- or, equivalently, the periodic trajectory of a Snell billiard. |
| title | Snell meets Fagnano. Path optimization through an imperfect mirror |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.02236 |