MathDB

Inside the regular

n

-gon

M

with side

a

there are

n

equal circles so that each touches two adjacent sides of the polygon

M

and two other circles. Inside the formed "star", which is bounded by arcs, these

n

equal circles are reconstructed so that each touches the two adjacent circles built in the previous step, and two more newly built circles. This process will take

k

steps. Find the area

S_n (k)

of the "star", which is formed in the center of the polygon

M

. Consider the spatial analogue of this problem.

Problem Statement