Huang-ti of the 27th Century BCE is considered to be the first patron of mathematics, because he supported the studies of mathematics in China.  The mathematical interests that caused the Chinese to make so many advancements stemmed from their philosophical basis in mathematics.  The Chinese believed that numbers had "philosophical and metaphysical properties."  They used Numbers "to achieve spiritual harmony with the cosmos."  The ying and yang, a philosophical representation of harmony, show up in the I-King, or book of permutations, in a number system of 8 figures where '--'  is the male yang, and '- -' is the female ying.  These figures can be seen as representations in the binary number system if yang is considered to be one and ying is considered to be two.  With so many philosophical attachments to mathematics and numbers, it is not surprising that the Chinese accomplished so much in their discoveries in mathematics.

The Chou-pei is one the oldest Chinese mathematical work.  A possible date of the Chou-pei is 1105.  However, we are not totally sure of many dates in the history of Chinese math because much of it was recorded on bamboo, which deteriorated.  Also, many records were destroyed by new leaders and  re-recorded from memory, a fact that lends itself to suspicion of dating errors.  The Chou-pei showed up in Ancient China (a time period from 2000-600 BCE) probably sometime between the Shang dynasty and the Tang Dynasty.
 
The Chou-pei figure is constructed from a square, say for example, the square ABCD, which is of length one in the figure.  A line is extended from the side AB such that A is still an endpoint and it is extended three units so the final length of this line is four units.  Then a line is extended from BC in a similar fashion such that B is the endpoint and the final line is of length one unit.  Again, a line is extended from CD in the same way with C as the endpoint and from DA so that D is the endpoint.  Then the extended endpoints are connected by lines so that four right triangles are created, each with leg lengths of 3 and four.

This figure had been used to look at how one could know that a 3, 4, 5 triangle, or any triangle similar to it, would make a right triangle with out the knowledge of Pythagorean theorem.   Since, each triangle has an area of (1/2)(l)(h) in this figure each triangle has an area of (1/2)(3)(4) or 6.  Since there are four triangles with an area of 6 and one original square of area (1)(1)=1, then the total area of the large square is 25 meaning that each triangle has a hypotenuse or 5, since every side of the square must be 5.

This is an interesting way to look at right triangles with out the use of Pythagorean mathematics.  It is assumed that there were other applications of this figure, having to do with a calendar, for example.  This is just one of the interesting things about the Chou-pei, a Chinese mathematical discovery, figured to be older then the Arithmetic in Nine Sections.

Author: Maggie Cooper

References:
Eves, Howard, An Introduction to the History of Mathematics, 6th ed, Saunders College Publishing, 1990.

Chao, Jui-ling, "Mathematical Journey 3000 BCE-CE", <http://nunic.nu.edu/~frosamon/history/bc3000.html>, 1996.

Holland, Lai, and Chan, "Chinese Mathematics", <http://www.interlochen.k12.mi.us/math/AdvMath97.html>, 1997.