Why Do Shapes Fit Together So Nicely Sometimes?

Shapes can fit together like a puzzle if their edges match up perfectly. Think of playing with tiles on the floor, some pieces just slide into place because they are the right shape, but others leave little gaps that you have to fix with another tile.

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Examples

A floor made of square tiles fits together nicely with no gaps.
Hexagon-shaped honeycombs fit perfectly without leaving space between them.
Triangular cookie cutters can be arranged to cover a whole sheet of dough.

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Categories: Math · geometry· tiling· patterns· mathematics