Moser Circle Regions and Concurrence
The familiar doubling pattern breaks at six circle points, and one hidden concurrence changes the count again.
Free theory articleThe familiar doubling pattern breaks at six circle points, and one hidden concurrence changes the count again.
Concept & interpretation
The problem of finding the maximum number of regions created by connecting n points on a circle with straight chords is a classic example in mathematics illustrating the danger of early extrapolation.
Experiment
You can interact with a live model to observe these patterns and the effects of concurrences:
Experiment with the following steps:
- Set Circle points to 5 and verify that the actual regions count is 16.
- Set Circle points to 6 and Configuration to "Generic" to see 31 regions.
- Change the Configuration to "Central symmetry". Notice that three chords now intersect at a single central point.
- Observe that the distinct interior crossings drop to 13 and the actual regions drop to 30, creating a concurrence deficit of 1.