雙語科技百科(數學) 第35期:《周髀算經》
Zhoubi Suanjing
The oldest mathematical classic in China, Zhou,bi Suanjing or The Arith-metical Classic of the Gnomon and the Circular Paths of Heaven,is an astronomy text as is thought to have been compiled sometime between 500 BC and 200 ng the Tang Dynasty, the book was listed as the first of all the texts included in the Ten, Mathematical contains some important mathe-matical sections and measures the positions of the heavenly a gno-mon might be used is described in a conversation between Duke of Zhou and his as astrologer Shang Gao in the text:
《周髀算經》是中國歷史上最早的一部數學典籍，也是一部天文學著作。成書時間大約在公元前5世紀與公元2世紀之間，唐代被收入《算經十書》，並被列爲《十經》的第一部。該書包括許多重要的數學內容，還對天體方位作了測定。例如書中周公與商高的一段對話描述瞭如何用日圭標竿進行測量：Duke of Zhou: How great is the art of numbers? Tell me something about the application of the gnomon.
周公日：“大哉言數！請問用矩之道？”
Shang Gao: Level up one leg of the gnomon and use the other leg as a plumb line. When the gnomon is turned up, it can measure height; when it is turned o-ver, it can measure depth and when it lies horizontally it can measure lve the gnomon about its vertex and it can draw a circle; combine two gno-mons and they form a square.
商高日：“平矩以正繩，偃矩以望高，覆矩以測深，臥矩以知遠，環矩以爲圓，合矩以爲方。”Zhoubi Suanjin,g is a collection of 246 problems encountered during the conver-sations between the Duke of Zhou and Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm. The author of the Zhou-bi Suanjing writes that Emperor Yu quells floods, deepens rivers and streams, sur-veys high places and low places by using the Gougu rule. And this book contains one of the first recorded proofs of the Gougu rule, or the Pythagorean Theorem in the world.
《周髀算經》中周公與商高之間的對話涉及246個問題，每個問題都以相應數學算法得到解決。其中談到了勾股定理（亦稱畢達哥拉斯定理）及其在測量上的應用，記載了大禹如何運用勾股定理治理水災、加深河牀、測量高低。這是世界上關於勾股定理最早的文字記錄之一。The text of the Zhoubi Suanjin,g also explains that the reason that mathematics can be applied to so many different cases i-s as a result of the way that mathemati-cal reasoning allows one to pass from particular to general situations. This realiza-tion of the abstract nature of mathematics is important.
《周髀算經》還解釋了數學在各方面廣泛應用的一個原因，即數學推理使人們能夠從個別推及普遍，這是對抽象的數學性質的一個重要認識。Zhoubi Suanjin,g contains calculations of the movement of the sun through the year as well as observations of the moon and the stars, particularly the pole star.
此外，《周髀算經》還計算了太陽在一年內的運動，並對月亮和星星，尤其是北極星作了觀察。
