# Squaring the square

## Mathematical problem / From Wikipedia, the free encyclopedia

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**Squaring the square** is the problem of tiling an integral square using only other integral squares. (An **integral square** is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be **perfect**, meaning the sizes of the smaller squares are all different. A related problem is **squaring the plane**, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling. The order of a squared square is its number of constituent squares.