Definition:Parker Square

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The Parker square is array of dimension $3 \times 3$ whose elements are square number which is almost, but not quite, a magic square:

$\begin{array}{|c|c|c|} \hline 29^2 & 1^2 & 47^2 \\ \hline 41^2 & 37^2 & 1^2 \\ \hline 23^2 & 41^2 & 29^2 \\ \hline \end{array}$

Its rows, columns and main diagonal all add up to $3051$.

However, its other diagonal adds up to $4107$.

Also, there are $3$ repeated elements: $1^2$, $29^2$ and $41^2$, while the elements of a magic square are supposed to be unique.

Hence, while it is not actually a magic square, it is a near miss.

Source of Name

This entry was named for Matthew Thomas Parker.

Historical Note

The Parker square was discovered by Matt Parker in $2016$ when he was exploring to see how close it was possible to get to a magic square using all square numbers.

Note that it had already been proved that such a magic square would contain elements that are all over $10^{14}$.

The exercise here was nothing more than just having a go and seeing what would happen.

Unfortunately, to Matt Parker's chagrin, this attempt was videoed, named and became a widespread internet meme.

Parker is working as hard as he can to convert the Parker square into (in his words):

a mascot of the importance of giving something a go, even when you're likely to fail.