Background behind Pythagorean derivation

At this early point in Chinese history the model of the ancient Chinese equivalent of Heaven, 天 Tian, was symbolized as a circle and the earth was symbolized as a square. In order to make this concept easily understood the adopted symbol of the heavens was the ancient Chinese chariot. The charioteer would stand in the square body of the vehicle and a "canopy", the equivalent of an umbrella, stood next to them. The world was thus likened to the chariot in that the earth, the square, was where the charioteer stood, and heaven, the circle, was suspended above them. The concept has thus been termed "Canopy Heaven", 盖天 (Gaitian).

Eventually the populace began to turn away from the "Canopy Heaven" concept in favor of the concept termed "Spherical Heaven", 浑天 (Huntian). This was partly due to the fact that the people were having trouble accepting heaven's encompassment of the earth in the fashion of a chariot canopy because the corners of the chariot were themselves relatively uncovered. In contrast, "Spherical Heaven", Huntian, has Heaven, Tian, completely surrounding and containing the Earth and was therefore more appealing. Despite this switch in popularity, supporters of the Gaitian "Canopy Heaven" model continued to delve into the planar relationship between the circle and square as they were significant in symbology. In their investigation of the geometric relationship between circles circumscribed by squares and squares circumscribed by circles the author of the Zhoubi Suanjing deduced one instance of what today is known as the Pythagorean Theorem.

起源

《周髀算经》原名《周髀》，出现于西汉时期，记载相关天文学和数学的发展成果，尤其在数学方面有著突破性的进步，后人认为是经典之作，因此则改称为《周髀算经》。

内容

「周髀」这个名称，按该书中的解释，「周」指的是周代，指从周代传下来的一些方法，「髀」原意指的是股（大腿）或者股骨，在这里的意思是「用来测量日影的长八尺之表」。

天文学

天文学方面，《周髀》主要阐述盖天说和四分历法。

数学

数学方面，《周髀》主要记载汉代的数学成就，率先提出了几何学重要的勾股定理，并在测量太阳高远的方法中给出勾股定理的一般公式。

《周髀》中出现运用重差术绘出的日高图，不过没有详细说明方法，三国时，赵爽、刘徽进一步研究，使之成为中国古代测望理论的核心内容。

《周髀》周就是圆，髀就是股。上面记载周公与商高的谈话，其中就有勾股定理的最早文字记录，即「勾三股四弦五」，亦被称作商高定理。事实上这一定理在时间上还应往前推移。

地理学

地理学方面，《周髀》明确阐述了极昼和极夜现象。

价值

《周髀算经》的作者已经无法得知，从成书时间来看，并非一人一时之作，而是对先秦数学发展成果的总结。

《周髀算经》是中国流传至今最早的数学著作，是后世数学的源头，其算术化倾向决定中国数学的性质，历代数学家奉为经典。

《周髀算经》的采用最简便可行的方法确定天文历法，揭示日月星辰的运行规律，囊括四季更替，气候变化，包涵南北有极，昼夜相推的道理。给后来者生活作息提供有力的保障，自此以后历代数学家无不以《周髀算经》为参考，在此基础上不断创新和发展。

日高与七衡