Magic circle (mathematics)

Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameter are identical. One of his magic circles was constructed from 33 natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center.

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. His magic circle series includes: magic 5 circles in square, 6 circles in ring, magic eight circle in square magic concentric circles, magic 9 circles in square.

Yang Hui's magic concentric circle has the following properties

64 numbers arrange in circles of eight numbers, total sum 2080, horizontal / vertical sum =260.

${\displaystyle 40+24+9+56+41+25+8+57=260}$

${\displaystyle 14+51+46+30+3+62+35+19=260}$

${\displaystyle 45+29+4+61+36+20+13+52=260}$

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