Home | Fitting things together

The geometry of fitting things together




A photo essay about shapes fitting together to make patterns, and spaces divided into patterns of shapes.


Some shapes fit together into a tight stack, with no gaps between them.

But stacking some shapes—spheres, for example—creates tiny gaps between them.

With shapes that fit together perfectly—something called tessellation—you can stack them endlessly with no wasted space.

For centuries, artists have explored symmetrical patterns in tessellations.

Natural systems follow the same geometric rules for using space efficiently, and they create beautiful patterns in the process.

When plants need to pack a lot into a tiny space, they can generate highly ordered patterns, such as this one based on the Fibonacci series of numbers.

Even where space is less constrained, as in this cracked mud surface, nature still follows geometric rules for fitting things together to expend the least amount of energy.

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Fitting things together exhibits link
Exhibits about shapes fitting together to make patterns, and spaces divided into patterns of shapes.

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Geometry Playground is made possible by the National Science Foundation and the Gordon and Betty Moore Foundation.

Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

National Science Foundation Gordon and Betty Moore Foundation

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