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arXiv · 2110.11691

Return of the plane evolute

Ragni Piene·Cordian Riener·Boris Shapiro
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Abstract

Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree $d\ge 2$, we provide lower bounds for the following four numerical invariants: 1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree $d$; 2) the maximal number of real cusps which can occur on the evolute of a real-algebraic curve of degree $d$; 3) the maximal number of (cru)nodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree $d$; 4) the maximal number of (cru)nodes which can occur on the evolute of a real-algebraic curve of degree $d$.

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Ragni Piene, Cordian Riener, Boris Shapiro. 2021-10-22. Return of the plane evolute. https://arxiv.org/abs/2110.11691

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