Methods of Information Geometry (Translations of by Shun-Ichi Amari, Hiroshi Nagaoka

By Shun-Ichi Amari, Hiroshi Nagaoka

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Extra resources for Methods of Information Geometry (Translations of Mathematical Monographs 191)

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Bai Shangshu lap]. 1982. Cong Wang Mang liang qi dao Liu Xin yuan lu [cr] [From Wang Mang's measuring vessel to Liu Xin's ratio of circumference to diameter]. 2, 75-79. - - - 1983. Jiu zhang suanshu zhushi [cs] [Annotations on Nine chapters of the mathematical art]. Beijing: Kexue chubanshe. 33 HM 13 CIRCLE MEASUREMENTS 339 Beckmann, P. 1970. A history of 7T (pi). : Golem, 1971. Gupta, R. C. 1975. Some ancient values of pi and their use in India. Mathematics Education 9, 1-5. He Shaogeng [bbl. 1983.

8. For an objective review of the polemic of this problem, see [Li Di 1982, 35-44]. 9. For a brief biography of Zu Chongzhi, see [Li Di 1962]. See also [Ruan Yuan 1799353,91-105]. 10. See [Qian 1923, 59; Yan 1936b, 43; Sun 1955, 9]. II. For a brief survey of this period, see [Xu 1957, 48]. 12. Thc diagram is missing, but it should be similar to Fig. I. 13. For the square-root extraction procedure, see [Wang & Needham 1955, 350-356; Lam 1969, 93-97]. REFERENCES Ang Tian Se. 1977. Chinese computation with the counting-rods.

This is why half the circumference multiplied by the radius is the area of the circle. The relation of circumference and diameter considered in this manner gives the most satisfactory result. The ratio of circumference to diameter is in fact not 3 to I. The figure 3 attached to the circumference actually means that the perimeter of an inscribed hexagon is three times the diameter. , 3] is used to compute the length of an arc, the result obtained is not the arc but the chord. The value of this ratio was, however, passed on from generation to generation indicating the reluctance of the people to strive for accuracy.

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