Complex numbers and plane geometry

The representation of complex numbers as points of the Euclidean plane naturally leads to a two-way interaction between geometry and numbers. The geometry of the plane has a very deep influence in the study complex analytic functions. In this article, we illustrate the other way aspect by a few simple-minded application of complex numbers to give elegant solutions of problems in plane geometry, such as Ptolemy’s Theorem, Euler-line and Nine-point Circle Theorem. Anant R Shastri is a Professor at IIT, Bombay. His research inerests are in algebraic topology and algebraic geometry. He is also keen in math education and music. This article is based on a talk given to an audience consisting mainly students of class IX and X, at Nehru Science Centre under the aegis of Bombay Association for Science Education and Bombay Math. Colloq. on 25th Jan. 2003. An earlier version of this article was published in Bona Mathematica, Vol.14 Nos.1–2, 2003.     

后现代主义语境下的通俗小说——浅论阿瑟·阿萨·伯格的推理小说

以通俗小说作为理论的载体是当代美国大众传播理论家和通俗文化学者阿瑟·阿萨·伯格的一个另类创举。将神圣的理论、权威与学界的腐败、犯罪杂糅在一起,作者戏弄并挑战了理论和权威,也反映了他本人的某种心理投射。伯格的小说在一定意义上代表了21世纪西方文化的一种跨学科的多元倾向。     

二维预设逻辑和复句预设投射

二维预设逻辑是一种特殊的四值逻辑。在二维预设逻辑中,每个句子的赋值是二维的,包含句子本身的真值和句子预设的真值。用二维逻辑的真值表方法来分析语义预设投射,可以很好的解释语义预设投射的“累积”现象和“消去”现象。     

Does the amount of on-screen text influence student learning from a multimedia-based instructional unit?

The present study examines how changes in the amount of on-screen text will influence student learning from a multimedia instructional unit on basic concepts of coordinate geometry. The relative effectiveness of two different versions (short-text and whole-text) of the instructional unit was examined for students who differed in terms of their ability to remember symbolic units, symbolic systems and symbolic interpretations. A total of 101 seventh graders were randomly assigned to work with either the whole-text or the short-text version. Student gains were analyzed using pre-test, post-test and retention test scores. Memory ability was assessed by the sub-tests of the Structure of Intellect-Learning Abilities Test. Results indicated no significant differences between groups who worked with short-text and whole-text versions. However retention scores of high and low memory groups who worked with the whole-text version showed significant differences. The whole-text version was observed to favor students with high memory for symbolic implications. Results suggest that workability of design principles for multimedia instruction may depend on the nature of the task and characteristics of the learner.     

仿射不变量在初等几何中的应用

简要叙述克莱因(F.Klein)几何观点,介绍几个仿射不变量,探讨如何利用仿射变换中的不变量解决一些初等几何问题,体现了高等几何对初等几何有重要的指导意义。     

沿直边简支环扇形薄板弯曲问题的辛几何法

由平面弹性与薄板弯曲问题的相似性,本文在辛体系中以径向模拟为时间,研究了两直边简支时的环扇形板弯曲问题。利用分离变量和本征函数展开等方法,给出其一个分析求解法,本文所得的结论为辛本征解的应用研究以及相关问题的解析求解提供了理论基础。     

基于几何着色器的Lengyel轮廓毛发实现

在层状纹理切片表达真实感短毛发的GPU实现方法中,模型轮廓处毛发切片的计算与生成需要消耗很大的显存,影响绘制效率。通过几何着色器进行边缘检测和生成Fin,改善轮廓处毛发切片渲染效率,则不必为边缘检测在每条边都加入退化三角形到网格。与此前方法相比,显存几乎没有消耗,提高了绘制效率。     

分形曲线曲面的分形插值法及其与随机生成法比较

给出了矩形域上的分形插值数学模型,分形插值曲线曲面的MATLAB程序.应用实际的数据进行了分形插值曲线曲面的研究,并与随机生成法做了比较.这对直观显示复杂物体的几何形态,研究具有分形特征的地形地貌,断层表面和材料裂缝表面等,具有重要的理论意义和实用价值.     

检视新一轮数学课程改革的论争

新一轮数学课程改革在课程目标、课程内容、教学方式、教材编排方式和评价方式等方面发生了深刻的变革,这些变革促进了中小学数学教育的发展.不过,课程改革也出现了一些问题,引发了一些论争,如关于数学生活化的论争、关于数学"双基"的论争、关于学习方式转变的论争、关于几何课程改革的论争和关于教材编排方式的论争等.检视这些论争并对其进行理性思考,有助于推动课程改革健康发展.     

数学实验中计算机软件的应用与拓展

阐述数学实验的思想理念和数学实验的具体做法.利用Matlab、几何画板、Mathematica进行数学实验,实现数学实验中计算机软件的应用与拓展.