7 ms·
According to http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html a cube of side 9.01 can fit 27 balls
by OscarCunningham 6y ago
According to http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html http://hydra.nat.uni-magdeburg.de/packing/scu/scu.html a cube of side 9.01 can fit 27 balls of diameter 3, but 100 balls of diameter 2. Since 27×3^3 = 729 and 8×2^3 = 800, the balls of diameter 2 are more efficient in this case.
- OscarCunningham 6y agoIn fact it seems that the diameter 3 balls are most efficient only for cubes of edge-length between 3 and 2+sqrt(2) = 3.414.... These are the sizes for which you can fit in 1 diameter 3 ball, but can't fit in 4 diameter 2 balls. Above that, diameter 2 balls are more efficient (except that a cube of edge-length 6 can fit in the same volume either way; 27 diameter 2 balls or 8 diameter 3 balls).
- Retric 6y ago> Since 27×3^3 = 729 and 8×2^3 = 800 I think you mean 100 x 2^3 = 800. But, yer correct that’s what I get from using a half remembered example without checking.