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What kinds of magic squares did Yang Hui describe?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

In his work Xu gu zhai qi suan fa (1275; "Selection of Strange Mathematical Methods in Continuation of Antiquity"), the Chinese mathematician Yang Hui described a variety of magic squares. Among these, he detailed a 10-by-10 magic square in which the numbers in each vertical and horizontal line sum to 505.1

While the term "magic square" generally refers to a matrix where rows, columns, and main diagonals produce the same constant sum, Yang Hui’s inclusion of these squares in his "Strange Mathematical Methods" highlights their historical significance as mathematical curiosities within the tradition of East Asian mathematics.231