The ratio of circumference to diameter by Zhang Heng. (Chinese. English summary) Zbl 0873.01004

Mo, Shaokui

J. Northwest Univ., Nat. Sci. 26, No. 4, 359-362 (1996).

It is well known that Zhang Heng (79–139) believed that \(\pi\) is approximately equivalent to the square root of 10. But the rationale of this crude equivalent is less well known. In fact, it comes from an approximation intended to derive the volume of the sphere given the area of the disk. All this has been previously explained in detail by D. B. Wagner (and later by others). Cf. D. B. Wagner [Liu Hui and Tsu Keng-chih on the Volume of the sphere, Chinese Sci. No. 3, 59–79].

Reviewer: J.-C.Martzloff (Paris)

MSC:

01A25

History of Chinese mathematics

Keywords:

Zhang Heng; \(\pi\); volume of the sphere