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This article introduces proximal Cech nerves and Cech complexes, restrictedto finite, bounded regions $K$ of the Euclidean plane. A Cech nerve is acollection of intersecting balls. A Cech complex is a collection of nerves thatcover $K$. Cech nerves are proximal, provided the nerves are close to eachother, either spatially or descriptively. A Cech nerve has an advantage overthe usual Alexandroff nerve, since we need only identify the center and fixedradius of each ball in a Cech nerve instead of identifying the three verticesof intersecting filled triangles (2-simplexes) in an Alexandroff nerve. As aresult, Cech nerves more easily cover $K$ and facilitate approximation of theshapes of irregular finite, bounded planar regions. A main result of thisarticle is an extension of the Edelsbrunner-Harer Nerve Theorem for descriptiveand non-descriptive Cech nerves and Cech complexes, covering $K$.

Proximal Planar Cech Nerves. An Approach to Approximating the Shapes of Irregular, Finite, Bounded Planar Regions