Abstract
This paper discusses the method of Liu Hui (3rd century) for evaluating the ratio of the circumference of a circle to its diameter, now known as π. A translation of Liu’s method is given in the Appendix. Also examined are the values for π given by Zu Chongzhi (429–500) and unsurpassed for a millenium. Although the method used by Zu is not extant, it is almost certain that he applied Liu’s method. With the help of an electronic computer, a table of computations adhering to Liu’s method is given to show the derivation of Zu’s results. The paper concludes with a survey of circle measurements in China.
Zusammenfassung
Dieser Aufsatz erörtert Liu Huis (3. Jahrhundert n. Chr.) Methode, das Verhältnis des Umfanges eines Kreises zu seinem Durchmesser zu berechnen, das heute als π bekannt ist. Der Anhang enthält eine Übersetzung von Lius Methode. Ebenso werden die Werte von Zu Chongzhi (425–500) für π geprüft, die tausend Jahre lang nicht überboten wurden. Obwohl die von Zu verwandte Methode nicht mehr existiert, ist es fast sicher, daß er sich Lius Methode bediente. Mit Hilfe eines elektronischen Rechners wird eine Berechnungstabelle beigefügt, die sich an Lius Methode anlehnt, um die Ableitung von Zus Ergebnissen zu zeigen. Der Aufsatz schließt mit einem Uberblick über die Kreismessungen in China.
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Lay-Yong, L., Tian-Se, A. (1986). Circle Measurements in Ancient China. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2736-4_5
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DOI: https://doi.org/10.1007/978-1-4757-2736-4_5
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