Block-Stacking Problem Has a Preposterous Solution You Need to See to Believe
12 days ago
- #engineering
- #physics
- #mathematics
- A single block can balance with half its length over the table's edge before tipping.
- Stacking multiple blocks allows for an overhang determined by the harmonic series, theoretically extending infinitely.
- The center of mass must remain above the table for stability; each additional block contributes a smaller overhang.
- In practice, factors like irregular shapes and weight limit the overhang, but mathematically, it's unbounded.
- The harmonic series (1 + 1/2 + 1/3 + ...) diverges, meaning the overhang can grow indefinitely in theory.
- With 4 blocks, the top block can extend a full length beyond the edge (sum ≈1.042).
- Achieving larger overhangs (e.g., 2 block lengths) requires many more blocks (e.g., 31).
- Real-world constraints (e.g., air currents, weight) prevent infinite overhangs, but the math remains fascinating.