Block Collisions Count π: The Configuration Space View
Mass ratio M/m = 10
2k
→ Collisions = first k+1 digits of π
Mass Ratio M/m
1 (M/m = 1, k=0)
100 (M/m = 10², k=1)
10,000 (M/m = 10⁴, k=2)
1,000,000 (M/m = 10⁶, k=3)
Animation
Run Simulation
Real Space — Block Positions
Configuration Space — Path Tracing
0
Collisions
—
θ = arctan(√m/M)
—
⌊π/θ⌋ (predicted)
Collisions =
⌊π / θ⌋
where θ = arctan(√(m/M))
Counting:
—