数形结合思想的培养

数形结合是数学研究的重要方法之一,是转化的数学思想的重要体现,在数学教学中采用数形结合的方法,往往能达到化难为易的教学效果。常见的数形结合形式有"以形助数"和"以数辅形"两种。本文从函数、方程、不等式、复数和解析几何五个方面浅谈数学教学中数形结合思想的培养。     

咬“文”嚼“字”：唐代宫廷的器物分类法

以唐桥陵墓室内刻有编号的14块青条石的研究为依据,参照唐代诗人王建《宫词》中对于唐宫器物分类法的记载,可揭示出湮没已久的唐代宫廷《千字文》分类法。这是一种《千字文》与阿拉伯数字相结合的分类方法,它在实际使用中几经演变。发现这种分类法有助于判定唐代宫廷制造与民间制造的界限。     

基于初等微积分和解析几何的C方法

Chandezon的基于坐标变换的微分方法(C方法)是最简单和最通用的方法之一.然而,迄今为止,只有少数的人使用它,可能是因为,它是用传统的基本张量理论进行阐述的.文章重新阐述了C方法,而没有使用任何的张量理论方面的知识,这样可以使光学工程师更容易理解.     

画法几何在空间机构定位问题上的应用

在进行机构运动分析中,常需要确定机构中杆件的位置、速度和加速度等问题,若用数学分析法,计算往往十分复杂,甚至容易出错;采用画法几何图解法,解题速度快,概念清晰,在一定程度范围内有它的应用价值。     

正轴测坐标系参数的两个计算式

根据给定的轴间角计算轴向变形系数和根据给定的投影方向在正投影体系中的投影角计算轴向变形系数,从而在诸多正轴测投影表达方案中选出最佳表达方案.     

数学软件Maple V在高等代数与空间解析几何数学中的应用

本文基于高等代数与空间解析几何的教学实践活动,应用数学软件Maple V,逐步培养学生运用几何与代数相结合的方法分析问题和解决问题的能力。     

Proofs produced by secondary school students learning geometry in a dynamic computer environment

As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date.     

用数学软件研究几何不等式

用数学软件Mathematica 4研究一个关于三角形边长的几何不等式：（｜（a-b）（b-c）（c-a）｜/（a＋b）（b＋c）（c＋a）＜1/22.）这里a,b,c是△ABC的三边长,同时证明了上界是精确的.     

几何初步知识教学探究

几何初步知识是数学教学的主要内容之一 ,包括三个方面的内容 :概念教学、公式教学和应用题教学。在教学中要考虑到几何初步知识这一内容的特点、学生的可接受性 ,使学生更好地掌握知识、发展智力和提高学习能力     

Varying Retrieval Categoricity Using Hyperbolic Geometry

The paper proposes a Vector Space Model over the Cayley-Klein Hyperbolic Geometry (referred to as Hyperbolic Information Retrieval = HIR) using a similarity measure derived from the hyperbolic distance. It is shown that the proposed model is equivalent with the classical Vector Space Model using Cosine measure with normalized weighting scheme. It is also shown that the categoricity of the new retrieval system can be varied by only modifying the radius of the hyperbolic space and without using a different weighting scheme and similarity measure, which is not the case in the VSM, where the same effect can only be obtained by both changing the weighting scheme and similarity measure at the expense of a more costly computation. Experiments are also reported to demonstrate and support the ideas, and they show that categoricity in HIR can be varied more than O(n) faster, where n is the number of index terms, than in the VSM.