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Mathematical Treasures - Zhoubi suanjing

Author(s): 
Frank J. Swetz and Victor J. Katz

These two pages are from the Zhoubi suanjing (Arithmetical Classic of the Gnomon and the Circular Paths of Heaven), a Chinese book on astronomy and mathematics dated to approximately 100 BCE.  These images are from a Ming dynasty copy printed in 1603.  These diagrams were added to the original text at some point in an attempt to illustrate a dissection proof of the "Pythagorean Theorem", known by the Chinese as the Gougu theorem.  A complete English translation and analysis of the Zhoubi suanjing is given by Christopher Cullen in his Astronomy and mathematics in Ancient China: the Zhou bi suan jing (Cambridge University Press, 1995).  See, in particular, appendix one.

 

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On this page, the diagram on the right is usually called the "hypotenuse diagram" and illustrates the proof of the theorem in the 3-4-5 case.  The diagram on the left shows how a square of side 3 fits into a square of side 5.

 

 

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This diagram illustrates a square of side 4 fitting into a square of side 5.

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Zhoubi suanjing," Loci (January 2011)

Dummy View - NOT TO BE DELETED

Mathematical Treasures