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1.
采取例证分析、探讨交比尤其是调和比在初等几何中的应用,彰显了高等几何在论证方法、思考问题等方面具有的独特性、巧妙性和灵活性特点。旨在群论观点下进一步认识初等几何的内涵与外延,深刻理解高等几何对初等几何教学与研究的指导作用。 相似文献
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冯天祥 《重庆第二师范学院学报》2002,15(3):8-10
首先将交比转化为角的正弦值的比或三角形的面积比或分割比的比，然后用以解决点共线及线共点；解决有关线段的比或比例问题并完成某些著名几何命题的初等证明，体现高等几何与初等几何的相互渗透，架设初等几何与高等几何之间的一座桥梁。 相似文献
3.
问题 四面体ABCD中 ,点P、Q、R分别是面 ABC、 ACD、 BCD内的一点 ,求作一个截面 ,使其过P、Q、R三点 .作法及说明 :如图 (1 )、(2 ) .1 作直线CP交AB于E ,直线CQ交AD于F . 2 若直线EF与BD相交 ,设交点为K ,如图 1 ,连CK ,作直线PQ交CK于L ,再作直线LR交BC、CD分别于M、N两点 .若直线EF于BD平行 ,过C作BD的平行线 (如图 2 ) ,作直线PQ交此平行线于L ,再作直线LR交BC、CD分别于M、N两点 .此时 ,P、Q、R、M、N这五点均在同一平面内 .3 考虑三个平面ABC、平面ACD与平面MPQN ,它们两两相交 ,得三条交… 相似文献
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本文应用三元齐次线性方程组有非零解的充要条件是它的系数行列式为零的定理,对两道几何竞赛题应用构造方程组法进行巧证.例1 设 AM 是△ABC 中 BC 边上的中线,任作一直线分别交 AB、AC、AM 于 P、Q、 相似文献
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习题(仅就人教版初中几何第三册第117页B组第2题) 已知如图1,OA和OB是⊙O的半径,并且OA⊥OB,P是OA上任一点,BP的延长线交⊙O于Q,过Q点作⊙O的切线交OA的延长线于R.求证:RP=RQ. 相似文献
6.
交比、调和比在初等几何中的应用●山西省教育学院郭刘龙交比、调和比是射影几何的两个基本不变量，本文探讨它们在初等几何中的应用，目的在于沟通高等几何与初等几何的联系，充分发挥高等几何对初等几何的指导作用，从而使中学数学教师能从较高的观点，简捷而巧妙地处理... 相似文献
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圆锥曲线有很多优美的几何特征,随着对其研究的逐步深入,新的几何性质不断被发现.下面就是笔者新近发现的椭圆的一个独特性质.定理椭圆的长半轴为a,短半轴为b,中心为O,过椭圆上一点P作长轴的垂线交辅助圆于点A,B,延长半径OA交P点的法线于点C,半径OB交P点的法线于点D,则OC=a b,OD=a-b,CP=PD.图1证明如图1,分别以椭圆的长轴、短轴所在直线为x轴、y轴建立直角坐标系.设椭圆的方程为b2x2 a2y2=a2b2(a>b>0),辅助圆的方程为x2 y2=a2.设P点坐标为P(x0,y0),则b2x20 a2y20=a2b2,过切点P的法线方程为a2y0x-b2x0y=(a2-b2)x0y0.因为AB垂直于x… 相似文献
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十八世纪,法国数学家白朗松给出了一种“任意等分线段”[作线段AB的1/n(n∈N,n≥2)]的尺规作图法,被称之为“白朗松构造”.先前的证明要用到高等几何中的调和比,本文先介绍这种构造等分的方法,而后用数学归纳法(对等分份数n归纳)给出四种初等证明.1作法(1)如图1,以已知线段AB为一边作△OAB,作CD∥AB,交OA于C,交OB于D,连接BC.(2)连接AD,交BC于P2,作射线OP2,交AB于M2,M2B=1/2AB. 相似文献
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从一个求交比的例题分析了交比求解中常出现的错误解法,总结交比教学中应注意的事项,归纳出点列交比求解的方法。 相似文献
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纵观 2 0 0 2年江苏各地的中考试题 ,出现了一大批富有时代气息的几何试题 .这些试题构思独特 ,结构新颖 ,既利于初中数学教学 ,又利于为高一级学校选拔人才 .加强这些试题的研究 ,对于指导中考复习 ,能起到事半功倍的作用 .下面选取几个试题以飨读者 .1 方程和方程组在几何中的应用图 1例 1 已知 :如图 1,⊙ O1 与⊙O2 相交于点 A,B,过点 A的直线分别交⊙ O1 ,⊙ O2于点 C,D.E为AC上一点 ,直线 BE交⊙ O2 于点 F,交 AC于点 G.(1)求证 :CE∥ FD;(2 )若 E为 AC的中点 ,求证 :△ ECG∽△EBC;(3 )在“(2 )”的条件下 ,当 GFDF… 相似文献
11.
Grizzi F Franceschini B Fiamengo B Russo C Dioguardi N 《Journal of Zhejiang University. Science. B》2007,8(4):217-220
Hepatocellular carcinoma （HCC） remains one of the major public health problems throughout the world. Although originally associated with tumorigenic processes, liver angiogenesis has also been observed in the context of different liver inflammatory, fibrotic, and ischemic conditions. Here we investigate the fractal dimension as a quantitator of non-Euclidean two-dimensional vascular geometry in a series of paired specimens of primary HCC and surrounding non-tumoral tissue, and discuss why this parameter might provide additional information regarding cancer behavior. The application of fractal geometry to the measurement of liver vascularity and the availability of a computer-aided quantitative method can eliminate errors in visual interpretation, and make it possible to obtain closer-to-reality numerals that are compulsory for any measurement process. 相似文献
12.
宗杰 《蒙自师范高等专科学校学报》1989,(1)
本丈通过自己辅导、讲授《高等几何》课的教学实践,从论述《高等几何》(主要是“射影几何”)课程中包含的一些基本的数学思想及其在教学中的运用入手,对如何把握这门课程的主要内容、重点和难点,以利于取得较好的教学效果,提高教学质量谈了一点粗浅的认识和体会。 相似文献
13.
GRIZZI Fabio FRANCESCHINI Barbara FIAMENGO Barbara RUSSO Carlo DIOGUARDI Nicola 《Journal of Zhejiang University. Science. B》2007,(4)
Hepatocellular carcinoma(HCC) remains one of the major public health problems throughout the world.Although originally associated with tumorigenic processes,liver angiogenesis has also been observed in the context of different liver in-flammatory,fibrotic,and ischemic conditions.Here we investigate the fractal dimension as a quantitator of non-Euclidean two-dimensional vascular geometry in a series of paired specimens of primary HCC and surrounding non-tumoral tissue,and discuss why this parameter might provide additional information regarding cancer behavior.The application of fractal geometry to the measurement of liver vascularity and the availability of a computer-aided quantitative method can eliminate errors in visual interpretation,and make it possible to obtain closer-to-reality numerals that are compulsory for any measurement process. 相似文献
14.
This study aims to investigate a construct of reading comprehension of geometry proof (RCGP). The research aims to investigate
(a) the facets composing RCGP, and (b) the structure of these facets. Firstly, we conceptualize this construct with relevant
literature and on the basis of the discrimination between the logical and the epistemic meanings of an argument, then assemble
the content of RCGP from literature and propose a hypothetical model of RCGP. Secondly, mathematicians and mathematics teachers
are interviewed for their ideas on reading mathematical proof in order to enrich the content of RCGP. Adapting the phases
of reading comprehension in language, the content of RCGP is classified into six facets. Lastly, these facets are structured
using the hypothetical model and then justified by students’ performance in the facets of RCGP using the multidimensional
scaling method. The results sustain that the structure of facets can be characterized by this conceptualized model. 相似文献
15.
GRIZZI Fabio FRANCESCHINI Barbara FIAMENGO Barbara RUSSO Carlo DIOGUARDI Nicola 《Journal of Zhejiang University. Science. B》2007,8(4)
Hepatocellular carcinoma (HCC) remains one of the major public health problems throughout the world. Although originally associated with tumorigenic processes, liver angiogenesis has also been observed in the context of different liver inflammatory, fibrotic, and ischemic conditions. Here we investigate the fractal dimension as a quantitator of non-Euclidean two-dimensional vascular geometry in a series of paired specimens of primary HCC and surrounding non-tumoral tissue, and discuss why this parameter might provide additional information regarding cancer behavior. The application of fractal geometry to the measurement of liver vascularity and the availability of a computer-aided quantitative method can eliminate errors in visual interpretation, and make it possible to obtain closer-to-reality numerals that are compulsory for any measurement process. 相似文献
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Konstantinos A. Sdrolias Triandafillos A. Triandafillidis 《Educational Studies in Mathematics》2008,67(2):159-169
Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often
proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary
school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary
school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict
school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies
about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts
taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean
view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements
in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities
and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether
a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels. 相似文献
19.
随着信息技术的发展,计算机辅助教学优化了传统教学手段,改变了几百年来的一支粉笔、一块黑板的历史。它以生动的画面、形象的演示,给人以耳目一新的感觉。鉴于此,本文就几何画板如何在中学数学辅助教学中推广、怎样运用"粉笔 黑板 ‘几何画板’"进行数学教学推广,用动态的效果展现给学生,帮助学生在实际应用中把握科学的内在实质,培养其观察能力、解决问题的能力和发散性思维的能力。 相似文献
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在信息技术高度发达的时代,计算机辅助教学(CAI)使得一系列复杂、抽象的数学难题迎刃而解。文章主要就CAI在数学教学中的应用展开探索。 相似文献