24 citations · 143 across the 29 of their papers we have counts for
26 papers · 1 filter
A short proof of Ball's plank theorem
Arseniy Akopyan, Alexander Polyanskii
We give a short proof of the following theorem of K. Ball: If a centrally symmetric convex body is covered by finitely many planks, then the sum of their rel…
On the total perimeter of disjoint convex bodies
Arseniy Akopyan, Alexey Glazyrin
In this note we introduce a pseudometric on convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a shor…
The Beauty of Random Polytopes Inscribed in the 2-sphere
Arseniy Akopyan, Herbert Edelsbrunner, Anton Nikitenko
Consider a random set of points on the unit sphere in , which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polyto…
Billiards in ellipses revisited
Arseniy Akopyan, Richard Schwartz, Serge Tabachnikov
We prove some recent experimental observations of D. Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard po…
When different norms lead to same billiard trajectories?
Arseniy Akopyan, Roman Karasev
In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection la…
The Regge symmetry, confocal conics, and the Schläfli formula
Arseniy Akopyan, Ivan Izmestiev
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asympt…