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The 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.
It is the basis for solving higher-order equations in ancient China, and it also plays an important role in the development of mathematics. [9] The "equations" discussed in the Fang Cheng chapter are equivalent to today's simultaneous linear equations. The solution method called "Fang Cheng Shi" is best known today as Gaussian elimination.
Fangcheng (sometimes written as fang-cheng or fang cheng) (Chinese: 方程; pinyin: fāngchéng) is the title of the eighth chapter of the Chinese mathematical classic Jiuzhang suanshu (The Nine Chapters on the Mathematical Art) composed by several generations of scholars who flourished during the period from the 10th to the 2nd century BC.
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain.
Jade Mirror of the Four Unknowns, [1] Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, [2] is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. [3] Zhu advanced Chinese algebra with this Magnum opus.
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number.
Let x be the number of cocks, y be the number of hens, and z be the number of chicks, then the problem is to find x, y and z satisfying the following equations: x + y +z = 100 5x + 3y + z/3 = 100. Obviously, only non-negative integer values are acceptable. Expressing y and z in terms of x we get y = 25 − (7/4)x z = 75 + (3/4)x
Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of ...