Magic circle (mathematics)
Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298).
Yang Hui's magic circle series was published in his Xugu Zhaiqi Suanfa《續古摘奇算法》(Sequel to Excerpts of Mathematical Wonders) of 1275.
The circles are arranged in a 3×3 square grid with the center area open in a way that also makes the horizontal / vertical sum along the central columns and rows is 260, and the total sum of the numbers along both diagonals is 520.
In his magic circle with 6 rings, the unit numbers of the 5 outer rings, combined with the unit number of the center ring, form the following magic square: Method of construction: Arrange group 1,2,3,4,6,7,9 radially such that Cheng Dawei, a mathematician in the Ming dynasty, in his book Suanfa Tongzong listed several magic circles In 1917, W. S. Andrews published an arrangement of numbers 1, 2, 3, and 62 in eleven circles of twelve numbers each on a sphere representing the parallels and meridians of the Earth, such that each circle has 12 numbers totalling 378.
Additional spokes can be added by replicating the columns of the magic square.
