Tutte along with 3 of his compatriots at trinity college became the first to solve the problem of squaring the square – that is, tiling an integral square using only integral squares. a perfect squaring has component squares all of different size, and the lowest order perfect square is shown below:
why study chemistry if you’re gonna square squares?
a non-perfect solution to squaring the square is known as Mrs. Perkins’ Quilt, where the greatest common divisor of the side lengths of the squares is 1, i.e. relaxing the condition that each component square is a different size, you may now use an infinite number of 1×1 squares to square your quilt, but only one of any larger square, all of which must have prime side lengths. The Mrs Perkins’ Quilt problem involves finding the minimal number of pieces with which to square a quilt in this way.