17 citations · 51 across the 22 of their papers we have counts for
8 papers · 1 filter
Extension of the first mixed volume to nonconvex sets
Emmanuel Tsukerman
We study the first mixed volume for nonconvex sets and apply the results to limits of discrete isoperimetric problems. Let . Define $D_N (M)=\lim_{ε\down…
Remarks on the the circumcenter of mass
S. Tabachnikov, E. Tsukerman
Suppose that to every non-degenerate simplex Delta in n-dimensional Euclidean space a `center' C(Delta) is assigned so that the following assumptions hold: (i) The map that assigns…
Circumcenter of Mass and generalized Euler line
Serge Tabachnikov, Emmanuel Tsukerman
We define and study a variant of the center of mass of a polygon and, more generally, of a simplicial polytope which we call the Circumcenter of Mass (CCM). The Circumcenter of Mas…
Discrete Conics
Emmanuel Tsukerman
In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise…
Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos
Emmanuel Tsukerman
In a recent paper titled "The parbelos, a parabolic analog of the arbelos", Sondow asks for a synthetic proof to the tangency property of the parbelos. In this paper, we resolve th…
The Perpendicular Bisector Construction in -dimensional Euclidean and Non-euclidean Geometries
Emmanuel Tsukerman
The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this…
On Polygons Admitting a Simson Line as Discrete Analogs of Parabolas
Emmanuel Tsukerman
We begin by proving a few general facts about Simson polygons, defined as polygons which admit a pedal line. We use an inductive argument to show that no convex -gon, ,…
The Perpendicular Bisectors Construction, the Isoptic Point and the Simson Line of a Quadrilateral
Olga Radko, Emmanuel Tsukerman
Given a noncyclic quadrilateral, we consider an iterative procedure producing a new quadrilateral at each step. At each iteration, the vertices of the new quadrilateral are the cir…