66 citations · 567 across the 83 of their papers we have counts for
7 papers · 1 filter
Domes over curves
Alexey Glazyrin, Igor Pak
A closed piecewise linear curve is called integral if it is comprised of unit intervals. Kenyon's problem asks whether for every integral curve in , there is a do…
Acute triangulations of polyhedra and R^n
Eryk Kopczyński, Igor Pak, Piotr Przytycki
We study the problem of acute triangulations of convex polyhedra and the space R^n. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. W…
The discrete square peg problem
Igor Pak
The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, b…
Inflating the cube without stretching
Igor Pak
We give a simple proof of the following result: There exists a non-convex polyhedron whose surface is isometric to the surface of a cube of smaller volume.
A short proof of rigidity of convex polytopes
Igor Pak
We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.
The area of cyclic polygons: Recent progress on Robbins' Conjectures
Igor Pak
In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently,…