17 citations · 51 across the 22 of their papers we have counts for
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math.DS2015★ 1 cited
Iterating evolutes and involutes
M. Arnold, D. Fuchs, I. Izmestiev +2
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth cur…
math.DS2013
Polygonal Bicycle Paths and the Darboux Transformation
I. Alevy, E. Tsukerman
A Bicycle -gon is an equilateral -gon whose diagonals are of equal length. In this paper we consider periodic bicycle -paths, which are a natural variation in…
math.DS2012★ 17 cited
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…