Crates of Bottles

February 5, 2013

The other day I was looking at a crate of 12 water bottles, and looked at the wasted space between them. Why not use a honeycomb? or even other bottle shapes?

Well, let us have a mathematical look at bottle packing. A round bottle occupies a surface (at the bottom of the box) of S=\pi r^2 (for some radius r) in a square of 4r^2. The occupancy is therefore

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