This pattern breaks, but for a good reason | Moser's circle problem

Summary by Krater

This video explains Moser's circle problem, showing how the number of regions formed by chords connecting points on a circle initially follows powers of two before breaking the pattern, and resolves the discrepancy using planar graph theory and Pascal's triangle.

From the video

Answers: What is the solution to Moser's circle problem?

• Moser's circle problem
• Planar graphs
• Euler's characteristic formula
• Pascal's triangle

What it concludes

• The number of regions formed by n points connected by chords on a circle is given by the formula 1 + n choose 2 + n choose 4.
• Euler's characteristic formula states that for any planar graph, V - E + R = 2.
• The sum of the rows of Pascal's triangle equals powers of two because each number donates two copies of itself to the next row.