《数书九章》方程章及其算筹思想:以“遥度圆城”为例  

The equation chapter of Mathematical Treatise in Nine Sections and its thought of calculating and raising funds:based on"Yaodu Yuancheng"

作　　者：刘蓓 赵世恩[1] 殷明娥[3] LIU Bei;ZHAO Shi′en;YIN Ming′e(Elementary Education College,Capital Normal University,Beijing 100048;Beijing Chaoyang Normal Primary School,Beijing 100013;School of Mathematics,Liaoning Normed University,Dalian Shenyang 116029)

机构地区：[1]首都师范大学初等教育学院,北京100048 [2]北京市朝阳师范附属小学,北京100013 [3]辽宁师范大学数学学院,辽宁大连116029

出　　处：《首都师范大学学报（自然科学版）》2021年第4期16-20,共5页Journal of Capital Normal University：Natural Science Edition

摘　　要：中国古代算法思想中的"方程"源于"算筹".13世纪秦九韶提出正负开方术,并将其用于求解一元高次方程,为数值解多项式方程奠定了重要的发展基础.本文以《数书九章》第八卷"遥度圆城"为例,探讨了秦九韶正负开方术求解高次方程正根的解法,剖析了古今算法高次方程的求解步骤,验证了玲珑10次方程来历的猜想,并结合古今算法的差异和优势,探究如何树立正确的数学史观.The ancient Chinese algorithm thought contained in"equation"originates from"counting chips".In the 13th century,Qin Jiushao proposed positive and negative square method to solve higher order equations,which laid an important foundation for numerical solution of polynomial equations.In the case of the eighth chapter of The equation chapter of Mathematical Treatise in Nine Sections based on"Yao du Yuan cheng",the steps of ancient and modern algorithms to solve higher order equations are deeply analyzed,and the differences and advantages of ancient and modern algorithms and how to establish a correct view of ancient mathematics history are explored.

关 键 词：方程 数书九章 算筹 正负开方术 

分 类 号：G65[文化科学—教育学]