100 random chords, how many intersections?
3Blue1Brown
Jun 16, 2026
Calculating intersection points for random chords requires precise definitions to avoid Bertrand's paradox. By selecting two points uniformly along the circle's circumference, you create a consistent model where the expected number of intersections follows a predictable mathematical pattern. This approach transforms a seemingly ambiguous geometric problem into a solvable exercise in probability.
Key insight: Bertrand's paradox proves that 'choosing a random chord' is mathematically ill-defined without specifying the exact method of selection, as different distributions yield different probabilities.
