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I wasn't referring to the reddit page, but the Wikipedia page it's based on: > Si-yüan yü-jian (《四元玉鑒》), or Jade Mirror of the Four Unknowns, was written by Zh
by leereeves 8y ago
I wasn't referring to the reddit page, but the Wikipedia page it's based on:
> Si-yüan yü-jian (《四元玉鑒》), or Jade Mirror of the Four Unknowns, was written by Zhu Shijie in 1303 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.[48]
If there's more to the story you might want to correct Wikipedia.
- fspeech 8y agoThe page I linked to is the actual page for Si-yüan yü-jian (《四元玉鑒》). The Wikipedia article you referred to may be slightly confusing but is not wrong. If you tried to solve a polynomial numerically, Horner's method would be handy. However we know there is no general solution per Abel and Galois.
- betterunix2 8y agoMore precisely, we know there is no general formula using basic arithmetic and radicals. Numerical methods count as a general solution as far as computer scientists are concerned (algebraic numbers are a subset of computable numbers).
- leereeves 8y agoWhich part are you're referring to when you say "The equations dealt with have been transcribed into modern algebraic expressions. They were definitely solved, not merely computed"?
- fspeech 8y agoThe page I linked to listed the problems posed and solved. The Chinese version is accompanied by modern notations using x,y,z... By the way the numerical solution to high order one variable polynomial was already known and given by another mathematician in an earlier (1247 AD) book: https://zh.wikipedia.org/wiki/%E6%95%B0%E4%B9%A6%E4%B9%9D%E7%AB%A0 https://zh.wikipedia.org/wiki/%E6%95%B0%E4%B9%A6%E4%B9%9D%E7...
- leereeves 8y agoI thought you were referring to a specific solution for a 14th degree polynomial. If you're just referring to the notation, that's a modern translation using modern notation. What was in the original?
- fspeech 8y agoI am saying all the equations listed also had their solutions given.
- leereeves 8y agoIt's not clear to me what's the original and what's a modern addition. For example: Mixed question Straight paragraph source Eighteen questions. Eighteenth question: Today, there is a sum of money and multiplication, and the product is reduced by the sum of the balances. It has a total of 170,162 steps. Only the cloud and the benefits. The fourth is Yifang, the third is from the low, the second is the benefit of the low, the first is the right, the three squares open, such as a quarter of the flat. Question, long, flat geometry? Answer: Ping is twelve steps and is thirty steps long. Li Tianyuan is the opening number and has: (equation) The solution is x=3, multiplied by four, which is the flat number. It seems to me that the text is the original Chinese (with only a numeric solution for one case) and the general equation is a modern addition.
- fspeech 8y agoI don't know what your confusion is. Every problem was given in the format of "Question, Answer, Steps to arrive at the answer" in the Chinese original. Numerically solving high order polynomials was already known so was not explained. The explanations were focused on elimination of variables for simultaneous equations (which can give you high order single variable polynomials).
- leereeves 8y agoIt might just be lost in translation, since I'm using Google Translate, but I don't see the "Question, Answer, Steps". I'll have to take your word for it.