Editing Chinese mathematics (section)

====''Jade Mirror of the Four Unknowns''====
[[File:Sixianghuiyuan.jpg|right|thumb|upright=1.1|Facsimile of the ''Jade Mirror of Four Unknowns'']]
The ''[[Jade Mirror of the Four Unknowns]]'' was written by [[Zhu Shijie]] in 1303&nbsp;AD and marks the peak in the development of Chinese algebra. The four elements, called heaven, earth, man and matter, represented the four unknown quantities in his algebraic equations. It deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of ''fan fa'', today called Horner's method, to solve these equations.{{sfn|Boyer|1991|loc="China and India"|p=203}}

There are many summation series equations given without proof in the ''Mirror''. A few of the summation series are:{{sfn|Boyer|1991|loc="China and India"|p=205}}

<math>1^2 + 2^2 + 3^2 + \cdots + n^2 = {n(n + 1)(2n + 1)\over 3!}</math>
<math>1 + 8 + 30 + 80 + \cdots + {n^2(n + 1)(n + 2)\over 3!} = {n(n + 1)(n + 2)(n + 3)(4n + 1)\over 5!}</math>