Moser's Circle Problem

A common problem in Proof Writing to highlight how easy it is to assume incorrect Conjectures.

Definition

1. On a circle, with $n$ number of points, draw chords connecting each point to every other point.
2. The $n$ points should never be arranged in such a way that creates 3 chords intersecting at a same point
3. The number $r$ is the number of triangular regions created by the chords

Incorrect Assumption

From a glance, it appears that the pattern grows according to $R=2^{n-1}$