Quilt Notes: MAGIC SQUARE(S) is listed as #975 in Maggie Malone's 5,500 QUILT BLOCK DESIGNS. It is also included as #3065 in Barbara Brackman's ENCYCLOPEDIA OF PIECED QUILT PATTERNS, with a slight difference in the spacing, but basically the same pattern.
In terms of mathematics, the term "magic square" can also refer to a group of numbers in a block so that in every direction (even on the diagonal-wow!!) they add up to the number 15 as illustrated below. But it can be done visually also with geometric icons by way of counting up the dots in each of the linear figures, including the center dot (see illustration upper left in the side panel.)
The Chinese culture has something very similar, and very ancient, and they call it a LUO SHU SQUARE (for which see the article at Wikipedia, also called LO SHU Square).
A thought comes to mind as regards the fact that the number 5 is always in the center of the MAGIC SQUARES — everything centers and depends on it, no matter how the numbers are arranged around the perimeter. In China the number 5 is lucky. One website on Chinese culture says: "People with the lucky number 5 usually tend to pursue freedom...As for romantic relationships, they hold an open mind and long for love evolving from friendship. Their love affairs are usually based on a steady friendship, not love at first sight."
More oriental-inspired patterns at this site include: