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NOTE: This is a very broad, open problem raising many issues. It is best approached intuitively with a low level of mathematics and plenty of discussion and diagrams. It should provide much food for thought.
Certain flat shapes can fit together on a flat surface efficiently (i.e. using the least amount of space), whereas others leave lots of gaps when we try to pack them together.
Whilst it might seems relatively simple, the problem of 'shape packing' is very difficult mathematically to solve with certainty. Intuitive visualisation often works just as well as a strict mathematical analysis, and often is the only sensible possibility with packing together complicated shapes
In reality, complex molecules such as proteins pack, or fold, together in very intricate ways.