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The eye of Drosophila as a model system for studying intracellular signaling in ontogenesis and pathogenesis

Katanaev, V. ; Kryuchkov, M.

In: Biochemistry (Moscow), 2011, vol. 76, no. 13, p. 1556-1581

Iterating evolutes and involutes

Arnold, Maxim ; Fuchs, Dmitry ; Izmestiev, Ivan ; Tabachnikov, Serge ; Tsukerman, Emmanuel

In: Discrete & Computational Geometry, 2017, vol. 58, no. 1, p. 80–143

This paper concerns iterations of two classical geometric constructions, the evolutes and involutes of plane curves, and their discretizations: evolutes and involutes of plane polygons. In the continuous case, our main result is that the iterated involutes of closed locally convex curves with rotation number one (possibly, with cusps) converge to their curvature centers (Steiner points), and...