2 papers
math.DS2025
Snell meets Fagnano. Path optimization through an imperfect mirror
Maxim Arnold, Jaewoo Park
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 triangl…
math.NT2025
On Euclidean Algorithms for oriented linear Grassmanians
Maxim Arnold, Oleg Karpenkov
In this paper we study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmanians . We propose two algorithms: Maximal Element Eliminat…