In early 5th century AD，for deriving the cycle of the intercalary month in a calendar一making system，a numerical method was invented by Chinese Mathematician. With a constructed theorem，the author comes to a conclusion that this method，in a sense，equals to the algorithm of the continued fraction. A series convergent to any given number could be derived with this method. The result explains a fact，which has been verified being served as convergent to some constants，appeared in the texts of mathematics or astronomy in ancient China，but on evidence to show there was an algorithm of continued fraction in ancient China. By the use of this method，a possible way for deriving Zu Chongzhi’s value π=355/113 is demonstrated.
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