17 citations · 51 across the 22 of their papers we have counts for
6 papers · 1 filter
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…
On the discrete bicycle transformation
Serge Tabachnikov, Emmanuel Tsukerman
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the contin…
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 Edge-Isoperimetric Problem in
Emmanuel Tsukerman
We consider the edge-isoperimetric problem on the graph of the infinite grid in the metric. We first show that the solutions are not nested, so tha…
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, ,…