page_title: Magic circle (mathematics)
section_title: Yang Hui Magic Nine circles in a square
hierarchical_section_title: Magic circle (mathematics) / Yang Hui magic  circles / Yang Hui Magic Nine circles in a square
caption_attribution_description: English: Yang Hui magic circle 中文（简体）‎: 杨辉算法 连环图
context_page_description: Magic circles were invented by the Song dynasty Chinese mathematician Yang Hui. 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.
context_section_description: 72 number from 1 to 72, arranged in nine circles of eight numbers in a square; with neighbouring numbers forming four additional eight number circles: thus making a total of 13 eight number circles:
  Extra circle x1 contains numbers from circles NW, N, C, and W; x2 contains numbers from N, NE, E, and C; x3 contains numbers from W, C, S, and SW; x4 contains numbers from C, E, SE, and S.
  Total sum of 72 numbers = 2628;
  sum of numbers in any eight number circle = 292;
  sums of three circles along horizontal lines = 876;
  sum of three circles along vertical lines = 876;
  sum of three circles along the diagonals = 876.
caption: Yang Hui 9 magic circles in a square 连环图
exif: {"Image Make": "Canon", "Image Model": "MP620 series", "Image XResolution": "600", "Image YResolution": "600", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "MP Navigator EX 2.0", "Image DateTime": "2012:07:02 06:25:46", "Image Artist": "Picasa", "Image YCbCrPositioning": "Centered", "Image ExifOffset": "216", "Thumbnail Compression": "JPEG (old-style)", "Thumbnail XResolution": "72", "Thumbnail YResolution": "72", "Thumbnail ResolutionUnit": "Pixels/Inch", "Thumbnail JPEGInterchangeFormat": "576", "Thumbnail JPEGInterchangeFormatLength": "8704", "EXIF ExifVersion": "0221", "EXIF DateTimeOriginal": "2012:07:02 06:10:55", "EXIF DateTimeDigitized": "2012:07:02 06:10:54", "EXIF ComponentsConfiguration": "YCbCr", "EXIF FlashPixVersion": "0100", "EXIF ColorSpace": "sRGB", "EXIF ExifImageWidth": "1500", "EXIF ExifImageLength": "1332", "Interoperability InteroperabilityVersion": "[48, 49, 48, 48]", "Interoperability RelatedImageWidth": "4960", "Interoperability RelatedImageLength": "7016", "EXIF InteroperabilityOffset": "440", "EXIF FileSource": "Reflection Print Scanner", "EXIF WhiteBalance": "Auto", "EXIF ImageUniqueID": "5f782e3158741d72b33143b00979b72b"}