![]() ![]() each number occupies one position on circle.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: Yang Hui magic eight circles in a square ĭing Yidong magic circles – numbers on each circle (solid colour) sum to 200 and numbers on each diameter (dashed grey) sum to 325ĭing Yidong was a mathematician contemporary with Yang Hui. There exist 8 semicircles, where the sum of numbers = magic number 69 there are 16 line segments (semicircles and radii) with magic number 69, more than a 6 order magic square with only 12 magic numbers.The sum of all numbers on each circle (not including 9) = 2 × 69.The sum of 8 numbers plus 9 at the center = 147.The sum of the numbers on four diameters = 147,.Yang Hui's magic concentric circle has the following properties Magic concentric circles, magic 9 circles in square. His magic circle series includes: magic 5 circles in square, 6 circles in ring, magic eight circle in square 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. One of his magic circles was constructed from the natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center. It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameters are identical. ![]() Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. Yang Hui's magic concentric circles – numbers on each circle and diameter (ignoring the middle 9) sum to 138
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