To Geng (mathematician)

Zu Geng , also Zu Gengzhi, Zu Xuan, (* around 480 in Jiankang , † around 525) was a Chinese court official, astronomer and mathematician.

Zu Geng came from a family of court officials, mathematicians and astronomers of the early Song Dynasty in what is now Nanjing . His father was the mathematician Zu Chongzhi . From 504 he actively campaigned for the introduction of his father's calendar (Danning calendar), with which he was successful in 510.

His best-known result is in the appendix by Li Chunfeng (7th century) to Liu Hui's commentary on Jiu Zhang Suanshu , the determination of the diameter of a sphere for a given volume . In a first formulation of the solution to the exercise, his formula corresponded to a rough value of (that is, he set ) and more precisely to a value of (correspondingly ). As proof, he used a variant of Cavalieri's principle , like Liu Hui, who had previously shown by constructing a curvilinear reference block that another proposed formula for solving the problem was wrong. The reference body that Zu Geng used to derive the volume of the sphere consisted of the intersecting body K of two cylinders standing perpendicular to one another, each of which surrounded the sphere S. The intersection of K with horizontal planes was a square, which gave the sphere a circular area, which were in relation if the radius is set equal to 1, so that a relation resulted according to the principle of Cavalieri . In a second step, Zu Geng calculated the volume of K through elementary geometric considerations and application of the Pythagorean theorem, so that in the end it resulted. ${\displaystyle d}$ ${\displaystyle V}$ ${\displaystyle \pi =3}$ ${\displaystyle d=(2V)^{\frac {1}{3}}}$ ${\displaystyle \pi ={\frac {22}{7}}}$ ${\displaystyle V=d^{3}{\frac {11}{21}}}$ ${\displaystyle {\frac {4}{\pi }}}$ ${\displaystyle {\frac {V_{K}}{V_{S}}}={\frac {4}{\pi }}}$ ${\displaystyle V_{S}={\frac {4\pi }{3}}r^{3}}$

As an astronomer, he measured the angular distance from Pole Star to the north celestial pole with the gnomon .

He may be involved in the 11th century lost mathematical manuscript Zhuishu , which is usually attributed to his father. Parts of his astronomical work are preserved in the astronomical part of the history of the Su Dynasty (Suishu).

literature

• LY Lam, KS Shen: The Chinese concept of Cavalieri's principle and its applications, Historia Mathematica, Volume 12, 1985, pp. 219-228 (analysis of the derivation of Zu Geng of the volume of the sphere via the principle of Cavalieri).

Web links

• John J. O'Connor, Edmund F. Robertson :  To Geng (mathematician). In: MacTutor History of Mathematics archive .
• Entry on Geng in the Encyclopedia Britannica (Alexei Volkov)

Individual evidence

1. ↑ ^{a b} Approximate dates of life after the article about him by Volkov in the Encyclopedia Britannica