Packing Circles into Squares | Desmos

Optimal Packing

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Why would we have to use Pythagoras' theorem to calculate the coordinates of some of the circle centres in the Hexagonal and Optimal cases?

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How much unused space is there in each case?

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We could use similar schemes to pack tins into boxes or to stamp out the maximum number of metal discs/washers from a given sheet of metal, although in this case we would require a small gap between the discs.

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