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Regarding the direct application of the Gou Gu Theorem, which is precisely the Chinese version of the Pythagorean Theorem, the book divides it into four main categories: Gou Gu mutual seeking, Gou Gu integer, Gou Gu dual capacity, Gou Gu similar. Gou Gu mutual seeking discusses the algorithm of finding the length of a side of the right triangle ...
The Pythagorean theorem and de Gua's theorem are special cases (n = 2, 3) of a general theorem about n-simplices with a right-angle corner, proved by P. S. Donchian and H. S. M. Coxeter in 1935. [2] This, in turn, is a special case of a yet more general theorem by Donald R. Conant and William A. Beyer (1974), [3] which can be stated as follows.
The theorem is also useful on a more microscopic scale, in biology. Living systems, such as cells, can be analyzed thermodynamically. They are rather complex systems, where many energy transformations occur, and they often waste heat. Hence, the Gouy-Stodola theorem may be useful, in certain situations, to perform exergy analysis on such systems.
Fermat's last theorem Fermat's last theorem, one of the most famous and difficult to prove theorems in number theory, states that for any integer n > 2, the equation a n + b n = c n has no positive integer solutions. Fermat's little theorem Fermat's little theorem field extension A field extension L/K is a pair of fields K and L such that K is ...
An example of the elementary mathematics in the Suàn shù shū, the square root is approximated by using false position method which says to "combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the ...
Liu Hui (fl. 3rd century CE) was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art). [2] He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period (220–280 CE) of China.
Examples of the gnomon described in the work have been found from as early as 2300 BC and the Duke of Zhou, was an 11th-century BC regent and noble during the first generation of the Zhou dynasty. The Zhoubi was traditionally dated to the Duke of Zhou's own life [ 8 ] and considered to be the oldest Chinese mathematical treatise. [ 1 ]
For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry. In mathematical contexts, duality has numerous meanings. [ 1 ] It has been described as "a very pervasive and important concept in (modern) mathematics" [ 2 ] and "an important general theme that has manifestations in almost every area ...