Ninety-One as sums of Four SquaresDigital Print2018
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
The December 2018 cover of Mathematics Magazine.
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.
