Points on a ring: An interactive walkthrough of a popular math problem
a day ago
- #math-puzzles
- #probability
- #geometry
- Problem: Probability that 4 random points on a circle all land in the same half.
- Initial incorrect assumption: Fixed semicircle probability is 12.5% (1/8).
- Correct approach: Semicircle can move; probability is about 50%.
- Key insight: Only one anchor point can define a valid semicircle containing all points.
- Formula for n points: Probability is n/(2^(n-1)).
- Generalization: Works for arcs smaller than a semicircle and higher dimensions (e.g., hemispheres on a sphere).