  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.
