Definition:Parker Square
Definition
The Parker square is array of dimension $3 \times 3$, whose elements are square numbers, 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.
Sources
- 2019: Matt Parker: Humble Pi: So, what have we learned from our mistakes?