共查询到20条相似文献,搜索用时 15 毫秒
1.
Arsalan Wares 《International Journal of Mathematical Education in Science & Technology》2018,49(1):153-159
The purpose of this paper is to provide examples of ‘non-traditional’ proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these propositions. 相似文献
2.
Daniela Ferrarello Mario Pennisi 《International Journal of Mathematical Education in Science & Technology》2016,47(4):597-605
In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products. 相似文献
3.
4.
给出了《无尺作图》两个基本作图命题的直接作图,使两个基本作图命题实际作图过程中使用圆规的次数减少到13次和10次,完全抛开了《无尺作图》基础作图体系的其他命题,完成了基础作图体系的优化研究. 相似文献
5.
无尺作图的基础作图体系的简化 总被引:1,自引:1,他引:0
简化了《无尺作图》的原基础作图体系中七个作图命题的作图过程,便得:1.两个基本命题实际作图过程中使用圆规的次数从原来的约300次和200次都减少到100次以下;2.简化了的那些命题的逻辑推理更加简明精巧;3.整个体系中的命题个数减少两个,而且其逻辑结构与更加优美。 相似文献
6.
Zhongmin SHEN 《数学年刊B辑(英文版)》2006,27(1):73-94
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce Riemann-Finsler geometry, by which we establish Information Geometry on a much broader base, so that the potential applications of Information Geometry will be beyond statistics. 相似文献
7.
Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry. 相似文献
8.
In this article, we investigate the impact of the introduction of a dynamic geometry environment on mathematical thinking by identifying changes in discourse engendered by its introduction in a high school geometry class. Our focus is on the teacher, and we find significant differences between static and dynamic geometry in terms of the ways in which the teacher talks about geometric objects, makes use of visual artifacts and models geometric reasoning. Even though these changes have major implications for the geometry being studied, they are made only very implicitly in the classroom. 相似文献
9.
Projectively flat Finsler 2-spheres of constant curvature 总被引:2,自引:0,他引:2
R. L. Bryant 《Selecta Mathematica, New Series》1997,3(2):161-203
After recalling the structure equations of Finsler structures on surfaces, I define a notion of "generalized Finsler structure"
as a way of microlocalizing the problem of describing Finsler structures subject to curvature conditions. I then recall the
basic notions of path geometry on a surface and define a notion of "generalized path geometry" analogous to that of "generalized
Finsler structure". I use these ideas to study the geometry of Finsler structures on the 2-sphere that have constant Finsler-Gauss
curvature K and whose geodesic path geometry is projectively flat, i.e., locally equivalent to that of straight lines in the plane. I
show that, modulo diffeomorphism, there is a 2-parameter family of projectively flat Finsler structures on the sphere whose
Finsler-Gauss curvature K is identically 1. 相似文献
10.
以与首都师范大学的李克正教授对话的方式,通过其口简要介绍代数几何这门重要学科在我国的早期发展情况,详细回忆李克正教授在国外学习代数几何的过程,以及他回国后的教学与研究成果,并通俗地阐述代数几何方法对于解决重大数论问题所起的关键作用. 相似文献
11.
This paper is the third part of a series of papers whose aim is to use the framework of twisted spectral triples to study conformal geometry from a noncommutative geometric viewpoint. In this paper we reformulate the inequality of Vafa–Witten [42] in the setting of twisted spectral triples. This involves a notion of Poincaré duality for twisted spectral triples. Our main results have various consequences. In particular, we obtain a version in conformal geometry of the original inequality of Vafa–Witten, in the sense of an explicit control of the Vafa–Witten bound under conformal changes of metrics. This result has several noncommutative manifestations for conformal deformations of ordinary spectral triples, spectral triples associated with conformal weights on noncommutative tori, and spectral triples associated with duals of torsion-free discrete cocompact subgroups satisfying the Baum–Connes conjecture. 相似文献
12.
Victor Pambuccian 《Mathematical Logic Quarterly》1992,38(1):345-348
We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous. 相似文献
13.
Victor Pambuccian 《Mathematical Logic Quarterly》2001,47(1):129-136
In this paper we provide quantifier‐free, constructive axiomatizations for 2‐dimensional absolute, Euclidean, and hyperbolic geometry. The main novelty consists in the first‐order languages in which the axiom systems are formulated. 相似文献
14.
B.N. Cooperstein 《Journal of Algebraic Combinatorics》2001,13(1):15-28
The generating rank is determined for several GF(2)-embeddable geometries and it is demonstrated that their generating and embedding ranks are equal. Specifically, we prove that each of the two generalized hexagons of order (2, 2) has generating rank 14, that the central involution geometry of the Hall-Janko sporadic group has generating rank 28, and that the dual polar space DU(6,2) has generating rank 22. We also include a survey of all instances in which either the generating or embedding rank of an embeddable GF(2) geometry is known. 相似文献
15.
Peter Schreiber 《Mathematical Logic Quarterly》1993,39(1):131-132
The uniqueness of the parallel lines is independent from the analogous statement on parallel planes and the usual further axioms of three-dimensional affine geometry. MSC: 51A15, 03F65. 相似文献
16.
This communication compiles propositions concerning the spherical geometry of rotations when represented by unit quaternions. The propositions are thought to establish a two‐way correspondence between geometrical objects in the space of real unit quaternions representing rotations and geometrical objects constituted by directions in the three‐dimensional space subjected to these rotations. In this way a purely geometrical proof of the spherical Ásgeirsson's mean value theorem and a geometrical interpretation of integrals related to the spherical Radon transform of a probability density functions of unit quaternions are accomplished. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
17.
The Swedish mathematician Torsten Brodén (1857–1931) wrote two articles on the foundations of Euclidean geometry. The first was published in 1890, almost a decade before Hilbert's first attempt, and the second was published in 1912. Brodén's philosophical view of the nature of geometry is discussed and his thoughts on axiomatic systems are described. His axiomatic system for Euclidean geometry from 1890 is considered in detail and compared with his later work on the foundations of geometry. The two continuity axioms given are compared to and proved to imply Hilbert's two continuity axioms of 1903. 相似文献
18.
Arsalan Wares 《International Journal of Mathematical Education in Science & Technology》2013,44(3):351-358
The purpose of this article is to provide examples of ‘non-traditional’ theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The Appendix contains proof outlines for each theorem. 相似文献
19.
Alexander Engel 《Journal of Functional Analysis》2019,276(7):2103-2155
We revisit ?pakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology.We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with uniform K-homology and prove Poincaré duality between uniform K-theory and uniform K-homology on spinc manifolds of bounded geometry. 相似文献
20.
Bulent Guven Adnan Baki 《International Journal of Mathematical Education in Science & Technology》2013,44(8):991-1013
This article presents an exploratory study aimed at the identification of students’ levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry. 相似文献