关于Steiner-Lehmes定理的4个推广猜想的研究  

Research on four developed conjectures about Steiner-Lehmes theorem

作　　者：廖文访[1] 许明春[1] 

机构地区：[1]华南师范大学数学科学学院,广州510620

出　　处：《南京信息工程大学学报（自然科学版）》2009年第2期134-141,共8页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：国家自然科学基金(10771077)

摘　　要：著名的Steiner-Lehmes定理旨在一定条件下判断1个三角形是否为等腰三角形,而王彦海把题设条件替换成了各种形式,并提出了9个猜想.用吴方法和MMP软件证明了其中的3个,提出并解决1个新的猜想.余下的几个猜想由于题设条件转化成代数条件的多项式次数较高,MMP软件运行时间太长而未能得到期望的结果.The famous Steiner-Lehmes theorem is to determine whether a triangle under some conditions is isosceles or not. WANG Yanhai changed the conditions into other forms and gave nine conjectures. This paper proves three of them using Wu-method and MMP software, puts forward a new conjecture and solves it. The rest of the conjectures have not been proved because the degrees of polynomials are so high, when the geometrical conditions are changed to algebraic ones, that it causes MMP to operate too long a time and therefore cannot obtain the expected result.

关 键 词：Steiner—Lehmes定理 吴方法 MMP软件 

分 类 号：G633.62[文化科学—教育学]