高师《初等几何研究》教学现状调查思考

《初等几何研究》是高师院校培养中学数学师资所特有的课程。目前《初等几何研究》教学现状不容乐观。基于此,对山西省高师数学系《初等几何研究》教学现状进行了调查和分析,发现《初等几何研究》课程存在诸多问题。因此,需要提高学生对《初等几何研究》课程重要性的认识,激发其学习兴趣;与时俱进改革教学内容,满足学生的发展需求;提倡多样化的教学方法,贯穿启发式的教学思想;掌握现代化的教学手段,提高教学效果;建立多元化的考核评价机制,培养学生的研究能力和创新精神。     

关于笛卡尔解析几何的哲学背景

分析笛卡尔数学创造工作中的心灵直观因素与笛卡尔知识论核心的"直观—演绎"原则如何在他的数学工作"解析几何"的建立中的具体体现,说明笛卡尔的数学工作和他的哲学思想的结合.     

基于“几何画板”绘制双曲线

几何画板是一个优秀的专业学科平台软件,代表了当代专业工具平台类教学软件的发展方向。主要介绍使用几何画板画双曲线的几种作法:双曲线第一定义、双曲线第二定义、直角坐标方程、参数方程、极坐标方程,并给出每种作法的详细制作步骤。     

Mechanical behaviour of cross-country ski racing poles during double poling

The purpose of this study was to evaluate the behaviour of cross-country ski poles during double poling on a treadmill using three-dimensional kinematics. The results were compared with standard laboratory tests of the pole manufacturers. A total of 18 skiers were analysed at two speeds (85% and 95% of the maximal speed) at grades of 1.5% and 7%. Variables describing cycle characteristics, bending stiffness, bending behaviour, and trajectories of the pole markers were analysed. Triangular-shaped poles demonstrated the greatest stiffness and lowest variability in maximal bending. Softer poles demonstrated greater variability in bending behaviour and lost ground contact at high skiing speeds, which for some skiers resulted in failure to complete high-speed tests. Considerable variations in pole behaviour for similar poles between skiers were observed, which might be attributed to differences in technique, indicating that mechanical properties of the poles did not exclusively determine pole behaviour in the dynamic situation. The greatest magnitude of pole bending was in the middle part of the pole, which differed from the standard static pole analysis of the manufacturer. Increases in grade demonstrated the greatest effect on pole bending. Distinct differences from the pole manufacturers' laboratory measures were apparent, suggesting that basic pole testing might be adapted.     

基于微分几何理论的感应电机输入输出解耦控制

感应电动机是一个多变量、强耦合、非线性的控制对象。微分几何理论是目前分析非线性系统的一种很有效的数学工具。文章介绍了应用微分几何理论对感应电机转速和磁链进行解耦控制的方法,并对解耦控制系统进行了仿真,仿真结果验证了理论分析的正确性。     

A new fast algorithm for computing the distance between two disjoint convex polygons based on Voronoi diagram

INTRODUCTION To compute the minimum distance between two convex polygons or polyhedrons is often a main step of many applications, such as collision detection (Choi et al., 2006; Li et al., 2003), path planning. In order to reduce the time complexity of the algorithm as much as possible, the convex property must be applied fully. Edelsbrunner (1985) proposed an algorithm for computing the minimum distance between two dis- joint convex polygons. The algorithm takes O(logm logn) time, and …     

矩形薄板弹性弯曲统一求解方法

在分析角点求解条件完备性的基础上将矩形板弯曲划分为广义静定问题和广义超静定问题 .广义静定弯曲可以由板的平衡微分方程及四边边界条件直接求解 ,广义超静定弯曲可以由叠加法求解 .这种求解方法可以解决各种边界条件下 (包括简支边、固定边、自由边、自由角点、支柱角点 )的矩形板在任意荷载作用下 (包括板面上作用任意法向荷载 ,板边界上作用任意荷载 ,板自由角点上作用集中力 ,板边界及支柱角点发生任意位移 )的弯曲 .本方法可以将经典的纳维叶解和李维解法有机地统一起来 ,且收敛速度快 ,计算精度高 .     

Proofs through Exploration in Dynamic Geometry Environments

The recent development of powerful new technologies such as dynamic geometry software (DGS) with drag capability has made possible the continuous variation of geometric configurations and allows one to quickly and easily investigate whether particular conjectures are true or not. Because of the inductive nature of the DGS, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical concern. In this article we discuss the implications of the development of this new software for the teaching of proof and making proof meaningful to students. We describe how three prospective primary school teachers explored problems in geometry and how their constructions and conjectures led them see proofs in DGS. Constantinos Christou: Author for correspondence.     

高师院校几何教学的历史途径法

历史途径教学方法将传统数学课程的内容与数学史的观点和材料有机地结合起来,这种方法已经在国外取得较好的教学效果.利用这种方法重新组织高等师范院校相关几何课程的教学内容和教学方案是必要的也是可行的,且有助于学生更好地理解和掌握初等几何学.     

解析法在讨论财务管理杠杆作用中的应用

财务管理中的杠杆作用是研究杠杆利益和财务风险的重要方法之一,其基本原理相关书籍均采用公式推导和描述性说明,为使人们容易认识这种杠杆利益和风险及两者关系的存在,本文采用图示解析法进行讨论。