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0111 · Aug 200719922001200920182026
10 results for hypocycloids

Wirtinger curves provide a simplified method to compute fundamental groups of certain algebraic plane curves.

problem Computing the fundamental group of the complement of algebraic plane curves.
method Wirtinger presentation based on the real picture of the curve and application to hypocycloids.
result Wirtinger presentation provides the fundamental group for an infinite subfamily of hypocycloids, relating them to Artin groups.

Study of evolutes of polygons and curves in higher dimensions.

problem Understanding evolutes of spatial polygons and curves in higher dimensions.
method Analyzing iterations of evolute transformations and studying properties of evolutes for polygons and curves.
result Eigenvalues of the second evolute map have double multiplicity, and evolutes of certain curves are homothetic to the curves themselves.

In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that …

2007-08-02abs ↗pdf ↗