WOLFRAM|DEMONSTRATIONS PROJECT

Overlapping Circles

​
number of circles
2
3
4
5
6
7
8
9
10
11
12
multiplicity of overlap
0
1
total colored area
=
π-
3
3
2
percentage area
≃
4.325%
In this Demonstration, the gray circle is a unit circle centered at the origin, and
n
unit circles are placed evenly on its circumference. The area contained in regions with
p
overlapping circles is calculated and compared to the area of the bounding circle (the dotted circle) that has radius 2.