共查询到19条相似文献,搜索用时 109 毫秒
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三角是中学数学的重要内容之一,其基础主要是几何中的相似形和圆.研究方法主要是代数变形和图象分析.因此,三角的研究已经初步把代数与几何联系起来了.本文讲讲三角代换在竞赛中的应用. 相似文献
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向量是近代数学最基本的概念之,它具有代数形式和几何形式的“双重身份”.是沟逋几何、代数、三角等内容的桥梁.“平面向量”足高中数学知识体系的重要组成部分, 相似文献
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例说三角解析几何试题的复数解法汪民岳(安徽省泾县中学242500)复数沟通了代数、三角及几何之间联系.高考中有些三角、解析几何试题,应用复数知识去解,常常能获得明快,简捷解法.1应用复数运算的几何意义用三角试题1.1求三角函数值天。(1992年全国高... 相似文献
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Dieter Betten 《Journal of Geometry》1972,2(2):107-114
The Moulton planes can be characterized as 2-dimensional topological projective planes having a 4-dimensional collineation group, which fixes exactly one nonincident point-line-pair aw. We give a representation of these geometries on the real protective plane such that a and W coincide with the origin and the line of infinity. This representation shows that the collineation groups of nonisomorphic Moulton planes act differently, although they are isomorphic as topological groups. 相似文献
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Benjamin Vejnar 《Topology and its Applications》2012,159(5):1404-1408
We present a topological characterization of the Sierpiński triangle. This answers question 58 from the Problem book of the Open Problem Seminar held at Charles University. In fact we give a characterization of the Apollonian gasket first. Consequently we show that any subcontinuum of the Apollonian gasket, whose boundary consists of three points, is homeomorphic to the Sierpiński triangle. 相似文献
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Horst Szambien 《Journal of Geometry》1986,26(2):163-171
A concept of topological projective geometry is defined, which in contrast to the definitions given in [Mi] and [SÖ] does not contain any dimensional restrictions. Besides elementary properties it is shown in this paper that these topological geometries always possess a coordinatization over a uniquely determined topological division ring if the dimension is finite.Dedicated to Prof. Dr. Hanfried Lenz on his 70th birthday 相似文献
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A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Ω(η), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets. 相似文献
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O. V. Sipacheva 《Journal of Mathematical Sciences》2005,131(4):5765-5838
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《Computational Geometry》2005,30(2):129-144
A convex geometry is a combinatorial abstract model introduced by Edelman and Jamison which captures a combinatorial essence of “convexity” shared by some objects including finite point sets, partially ordered sets, trees, rooted graphs. In this paper, we introduce a generalized convex shelling, and show that every convex geometry can be represented as a generalized convex shelling. This is “the representation theorem for convex geometries” analogous to “the representation theorem for oriented matroids” by Folkman and Lawrence. An important feature is that our representation theorem is affine-geometric while that for oriented matroids is topological. Thus our representation theorem indicates the intrinsic simplicity of convex geometries, and opens a new research direction in the theory of convex geometries. 相似文献
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Maria Karmanova 《Geometric And Functional Analysis》2011,21(6):1358-1374
We develop a new approach to studying the geometry of Carnot–Carathéodory spaces under minimal assumptions on the smoothness
of basis vector fields. We obtain quantitative comparison estimates for the local geometries of two different local Carnot
groups, as well as of a local Carnot group and the original space. As corollaries, we deduce some results that are well-known
and basic for the “smooth” case: the generalized triangle inequality for d
∞, the local approximation theorem for the quasimetric d
∞, the Rashevskiǐ–Chow theorem, the ball-box theorem, and so on. 相似文献
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C.H. Marchi L.K. Araki A.C. Alves R. Suero S.F.T. Gonçalves M.A.V. Pinto 《Applied Mathematical Modelling》2013
The focus of this work is to verify the efficiency of the Repeated Richardson Extrapolation (RRE) to reduce the discretization error in a triangular grid and to compare the result to the one obtained for a square grid for the two-dimensional Laplace equation. Two different geometries were employed: the first one, a unitary square domain, was discretized into a square or triangular grid; and the second, a half square triangle, was discretized into a triangular grid. The methodology employed used the following conditions: the finite volume method, uniform grids, second-order accurate approximations, several variables of interest, Dirichlet boundary conditions, grids with up to 16,777,216 nodes for the square domain and up to 2097,152 nodes for the half square triangle domain, multigrid method, double precision, up to eleven Richardson extrapolations for the first domain and up to ten Richardson extrapolations for the second domain. It was verified that (1) RRE is efficient in reducing the discretization error in a triangular grid, achieving an effective order of approximately 11 for all the variables of interest for the first geometry; (2) for the same number of nodes and with or without RRE, the discretization error is smaller in a square grid than in a triangular grid; and (3) the magnitude of the numerical error reduction depends on, among other factors, the variable of interest and the domain geometry. 相似文献
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Bilâl Altay 《Journal of Mathematical Analysis and Applications》2007,336(1):632-645
The matrix domain of the particular limitation methods Cesàro, Riesz, difference, summation and Euler were studied by several authors. In the present paper, certain topological properties and β- and γ-duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes. 相似文献