Moser's circle problem
This is a somewhat famous problem, known as Moser’s circle problem:
Here’s Wolfram’s formulation:
Determine the number of pieces into which a circle is divided if n points on its circumference are joined by chords with no three internally concurrent.
A less jargony version is:
Draw n points on the circumference of a circle. Connect each pair of points with a straight line segment. What is the maximum number of regions that the circle can be divided into as a function of n?
A few examples:
For n = 2, it has 2 regions,
and for n = 3, it has 4 regions.Solution