MathDB

Consider a regular

n

-gon of side length 1. For each of its vertices, a circle of radius one is drawn centered at that vertex. The resulting figure, consisting of the polygon and the

n

circles, partitions the plane into

f(n)

finite, bounded regions. Find

\sum_{n=3}^{25} f(n).

The first term corresponding to

i=3

is shown; each of the various colors corresponds to a distinct region with

f(3)=10

. Note that the lines corresponding to the polygon are treated no differently than the arcs corresponding to the circles in counting regions.
Proposed by Hari Desikan (HariDesikan)

Problem Statement