24 citations · 143 across the 29 of their papers we have counts for
6 papers · 2 filters
-webs generated by confocal conics and circles
Arseniy Akopyan
We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the…
A tight estimate for the waist of the ball
Arseniy Akopyan, Roman Karasev
We answer a question of M. Gromov on the waist of the unit ball.
On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape
Arseniy Akopyan, Vladislav Vysotsky
We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that for any convex shape , there exist four poin…
On the Circle Covering Theorem by A. W. Goodman and R. E. Goodman
Arseniy Akopyan, Alexey Balitskiy, Mikhail Grigorev
In 1945, A. W. Goodman and R. E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii , , in the plane it is always poss…
Incircular nets and confocal conics
Arseniy Akopyan, Alexander I. Bobenko
We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the…
Some Remarks on the Circumcenter of Mass
Arseniy Akopyan
In this article we give new proofs for the existence and basic properties of the cirucmcenter of mass defined by V. E. Adler in 1993 and S. Tabachnikov and E. Tsukerman in 2013.