Ninety-One as sums of Four Squares Digital Print 2018

It is based on Lagrange's theorem that every positive integer can be expressed as a sum of four squares, although the decomposition is not unique. The integer 91 (the number of this 2018 volume) can be expressed as a sum of squares in 5 (the number of this December issue) ways: \begin{align*} 91 &= 3^3 + 3^2 + 3^2 + 8^2 \\ &= 1^1 + 4^2 + 5^2 + 7^2 \\ &= 4^2 + 5^2 + 5^2 + 5^2 \\ &= 1^2 +1^2 + 5^2 + 8^2 \\ &= 0^2 + 1^2 + 3^2 + 9^2. \end{align*}

### Background and Inspiration

This work was originally done for use as cover art for the December 2018 issue of Mathematics Magazine. This is the twentieth of 25 original artworks I created for the journal Mathematics Magazine during 2015–2019.

### Publication History

• Mathematics Magazine, Cover Art, Vol. 91, No. 5, December 2018.