Affine Properties of Convex Equal-Area Polygons

Details Affine Properties of Convex Equal-Area Polygons Affine Properties of Convex Equal-Area Polygons

2011-03-14

arxiv.org/abs/1103.2722v3

Mathematics

Differential Geometry

15 pages, 10 figures

Scientific paper

In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth curves almost uniformly with respect to affine length, convex equal-area polygons admit natural definitions of the usual affine differential geometry concepts, like affine normal and affine curvature. These definitions lead to discrete analogous of the six vertices theorem and an affine isoperimetric inequality. One can also define discrete counterparts of the affine evolute, parallels and the affine distance symmetry set preserving many of the properties valid for smooth curves.

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