Zhao Youqin and His Calculation of (pi)

The paper discusses the method used by Zhao Youqin (1271-?) in his treatise Ge xiang xin shu to confirm Zu Chongzhi's (429-500) approximate value 355\113 of (pi). Zhao Youqin inscribed a square into a circle and performed an iterative procedure of calculation of one side of a 2 n-sided inscribed polygon for n = 3, . . . , 14. Included is a biographical sketch of Zhao Youqin, who was an astronomer, mathematician, and physicist as well as a Taoist monk and alchemist. A translation of Zhao's description of his method is given in the Appendix. L'article presente la methode avec laquelle Zhao Youqin (1271-?) a confirme, dans son traite Ge xiang xin shu, la valeur approximative de 355\113 pour (pi) attribuee a Zu Chongzhi (429-500). Zhao Youqin utilise une procedure iterative pour calculer les cotes des polygones reguliers a 2 n cotes inscrits dans un cercle, n = 3, . . . 14. L'auteur donne une breve biographie de Zhao Youqin qui etait astronome, mathematicien, physicien, mais egalement taoiste et alchimiste. La traduction de la methode de Zhao est fournie dans l'Annexe. ABS1-2163