简牍算书一种特殊计算方法解析

A special computational method in excavated mathematical books on bamboo slips:An analysis and interpretation

简牍算书中有一种特殊计算方法,带有明显的凑数特征,没有算理可言,不具有普适性,暂不见于《九章算术》等传世数学文献.这种计算方法目前见于北京大学藏秦简《算书》、张家山汉简《筭数书》、岳麓书院藏秦简《数》,涉及“里田术”和“盈不足术”两类算题或术文,典型者共计四例.对这种特殊计算方法进行研究,有助于正确解读简牍算书某些算题,利于简牍数学文献整理研究,具有文献学价值;可以真实地反映中国传统数学在战国秦汉时期发展的原貌,具有数学史价值.

Six mathematical books on bamboo slips have been excavated and then fully or partially published in recent decades in China.They are dated to pre-Qin,Qin,and Han periods.In three of these books,ancient Chinese mathematicians used a special computational method to solve some given problems.This method is characterized with contriving numbers,and is not universal.By four typical examples of this type,this method is analyzed and interpreted in detail in this article.The study of this special computational method is helpful both for correctly interpreting related problems in these books,and for truly reflecting in some aspects how traditional Chinese mathematics evolved in the pre-Qin,Qin and Han periods.