张家山汉简《筭数书》体积算题及相关问题探析

Analysis of Volume Chapters in Suànshùshū——the book of Mathematics and Related Issues

《筭数书》含7个体积算题.将每个算题内容分解为题名、题文、答案和解题方法四个部分,并据题意给出相应的几何图、公式和算式,以助理解.讨论相关问题,认为:体积算题成题时代应该为春秋晚期至公元前186年闰九月或其后不久;体积算题的目的是为了解决老百姓和政府官吏在日常生活和管理中对体积计算的实际需要;算题以所求体积的实物来命名的方式从侧面反映了中国早期几何注重实用性的特点;体积算题所反映的数学成就表明我国数学在战国时代就达到了一个高点.

There are 7 volume chapters in Suànshùshū 筭数书(The Book of Mathematics).Each chapter is to be broken up into four parts:title,problem,answer and algorithmic rule(s),and for each chapter,a geometric figure,formula and operation are suggested to facilitate a better understanding.Related issues are discussed and it is believed that the origin of these chapters might date back to the period between the late Spring & Autumn period and intercalary September 186 BCE or very soon later,that these chapters are of utilitarian purpose for civilians and officials to manage daily calculation of volume,that the way the geometric figures were named after real objects witnesses abundance of early Chinese geometry in vividness,not in abstractness,and that the mathematical achievements behind these chapters reveal that Chinese mathematics once arrived at a climax as early as in the Warring States period.