浅谈中学数学教学中的反例

在新的<数学课程标准>中,要证明一个命题正确,必须经过严密的推论,而要否定一个命题,却只需要能举出一个与结论相矛盾的例子就行,这个与命题相矛盾的例子便称为反例.反例是简明有力的否定方法;反例是加深理解的重要手段;反例是纠正错误解答的常用办法;反例可以发现问题;构造反例是活跃思维的一种途径.     

蚕食鲸吞

不同的进食方式一个细嚼慢咽,一个大口吞食,这是蚕和鲸不同的吃饭方式。想一想,造成这种差异的原因是什么?没错,主要原因就是它们的身体构造不同。     

构造平行四边形证题例析

平行四边形具有对边相等、对角相等、对角线互相平分等性质.证明某些几何题时,若能巧妙地构造出平行四边形,就会化难为易、化繁为简,证明过程简捷. 现举例说明. 一、证两线段相等例1 已知:如图1,在四边形ABCD中,AB=DC, AD=BC,E、F在对角线AC上,且AE=CF. 求证:BE=DP.(河北省中考题) 证明:连结BD交AC于O,连结DE、BF. ∵AB=DC,AD=BC, ∴四边形ABCD是平行四边形.     

发挥想象构造情境

由于对物理情境的想象是理解和应用物理知识的基础，在实际的高考试题中，多数物理问题的解答都需要先对题目所设情境有一个清晰的想象，在此基础上再进行推理判断或数学运算。     

添加梯形辅助线方法探索

辅助线对处理复杂的图形问题非常重要．通过构造辅助线，复杂的图形可以分解成简单的图形．现以求解梯形问题为例与同学们共同研究．     

节能建筑外墙构造

介绍了目前节能建筑外墙体的几种构造做法和施工的技术要点。提出应加强夏热冬冷地区外墙体隔热构造措施的研究,积极推广采用混凝土空心砌块做墙体的节能建筑。     

构造全等三角形解四边形问题

全等三角形和四边形知识联系非常紧密，四边形的许多性质、定理都是用全等三角形知识导出的．因此，运用几何转换，适当构造全等三角形，有助于四边形问题的解决。     

Fuzzy Comprehensive Assessment Method to Determine Tectonic Stress Patterns

The tectonic stress patterns were determined by a fuzzy comprehensive assessment method. Data of in-situ survey and fault information were utilized in the method. First, by making pressure and tension in the directions of along-river, cross-river, shear clockwise, and shear counterclockwise , 26 types of tectonic stress patterns were presented. And the stress vector of each pattern was obtained with FE software by taking unit displacement as boundary load. Then, by taking the 26 types of tectonic stress patterns as index set and 3 main stresses as factor set and choosing various operators, comparison of directions of computational stress vector and survey stress vector was made and the most possible tectonic stress pattern was obtained. Taking the 26 types of tectonic stress patterns as index set and strike angle as factor set, comparison of relationships between formation of fault and tectonic stress was made,and the tectonic stress patterns were assessed with known fault information. By summarizing the above assessment results, the most impossible tectonic stress pattern was obtained . Finally an engineering case was quoted to validate that the method is more feasible and reliable than traditional empirical method.     

构造三元齐次线性方程组解题

本文介绍构造三元齐次线性方程组,应用其有非零解的充要条件是它的系数行列式为零的定理,对部分代数、几何、三角问题和著名的牛顿“牛吃草”问题进行巧思妙解。