找回密码
 To register

QQ登录

只需一步,快速开始

扫一扫,访问微社区

Titlebook: Geometry; A Metric Approach wi Richard S. Millman,George D. Parker Textbook 19811st edition Springer-Verlag Inc. 1981 Cartesian.Euclid.Geom

[复制链接]
查看: 27017|回复: 47
发表于 2025-3-21 16:51:22 | 显示全部楼层 |阅读模式
书目名称Geometry
副标题A Metric Approach wi
编辑Richard S. Millman,George D. Parker
视频video
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Geometry; A Metric Approach wi Richard S. Millman,George D. Parker Textbook 19811st edition Springer-Verlag Inc. 1981 Cartesian.Euclid.Geom
描述This book is intended as a first rigorous course in geometry. As the title indicates, we have adopted Birkhoff‘s metric approach (i.e., through use of real numbers) rather than Hilbert‘s synthetic approach to the subject. Throughout the text we illustrate the various axioms, definitions, and theorems with models ranging from the familiar Cartesian plane to the Poincare upper half plane, the Taxicab plane, and the Moulton plane. We hope that through an intimate acquaintance with examples (and a model is just an example), the reader will obtain a real feeling and intuition for non­ Euclidean (and in particular, hyperbolic) geometry. From a pedagogical viewpoint this approach has the advantage of reducing the reader‘s tendency to reason from a picture. In addition, our students have found the strange new world of the non-Euclidean geometries both interesting and exciting. Our basic approach is to introduce and develop the various axioms slowly, and then, in a departure from other texts, illustrate major definitions and axioms with two or three models. This has the twin advantages of showing the richness of the concept being discussed and of enabling the reader to picture the idea more
出版日期Textbook 19811st edition
关键词Cartesian; Euclid; Geometrie; Geometry; addition; boundary element method; concept; feeling; idea; inca; model
版次1
doihttps://doi.org/10.1007/978-1-4684-0130-1
isbn_softcover978-1-4684-0132-5
isbn_ebook978-1-4684-0130-1Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer-Verlag Inc. 1981
The information of publication is updating

书目名称Geometry影响因子(影响力)




书目名称Geometry影响因子(影响力)学科排名




书目名称Geometry网络公开度




书目名称Geometry网络公开度学科排名




书目名称Geometry被引频次




书目名称Geometry被引频次学科排名




书目名称Geometry年度引用




书目名称Geometry年度引用学科排名




书目名称Geometry读者反馈




书目名称Geometry读者反馈学科排名




单选投票, 共有 1 人参与投票
 

0票 0.00%

Perfect with Aesthetics

 

1票 100.00%

Better Implies Difficulty

 

0票 0.00%

Good and Satisfactory

 

0票 0.00%

Adverse Performance

 

0票 0.00%

Disdainful Garbage

您所在的用户组没有投票权限
发表于 2025-3-21 23:30:34 | 显示全部楼层
Plane Separation,Plane and the Hyperbolic Plane, do satisfy this new axiom. In the third section we shall prove Pasch’s Theorem, which gives an alternative formulation of the plane separation axiom in terms of triangles. This means that Pasch’s Theorem follows from the plane separation axiom and the plane separation axiom follows from assuming Pasch’s Theorem.
发表于 2025-3-22 03:07:03 | 显示全部楼层
0172-6056 ugh use of real numbers) rather than Hilbert‘s synthetic approach to the subject. Throughout the text we illustrate the various axioms, definitions, and theorems with models ranging from the familiar Cartesian plane to the Poincare upper half plane, the Taxicab plane, and the Moulton plane. We hope
发表于 2025-3-22 07:16:18 | 显示全部楼层
https://doi.org/10.1007/978-3-663-07180-8 the hyperbolic results. In the second section we will be concerned with the theory of similar triangles and proportion. The third section will cover certain classical results of Euclidean geometry, including the Euler Line, the Nine Point Circle, and Morley’s Theorem.
发表于 2025-3-22 09:59:29 | 显示全部楼层
发表于 2025-3-22 14:42:02 | 显示全部楼层
https://doi.org/10.1007/978-3-663-07177-8erent in any geometric sense. Furthermore, as we develop additional axioms to verify we will need a more tractable notation. For these reasons we introduce an alternative description of the Euclidean Plane, one that is motivated by ideas from linear algebra, especially the notion of a vector.
发表于 2025-3-22 18:38:47 | 显示全部楼层
https://doi.org/10.1007/978-3-663-04786-5 measures are defined in our two basic models. In the second section we shall develop a new model with some very interesting properties. In the third section, some of the basic results associated with angle measure are discussed. The last section is devoted to the technical details of verifying the existence of angle measure on ℝ. and ℍ.
发表于 2025-3-22 23:27:42 | 显示全部楼层
发表于 2025-3-23 05:25:16 | 显示全部楼层
发表于 2025-3-23 06:33:06 | 显示全部楼层
 关于派博传思  派博传思旗下网站  友情链接
派博传思介绍 公司地理位置 论文服务流程 影响因子官网 SITEMAP 大讲堂 北京大学 Oxford Uni. Harvard Uni.
发展历史沿革 期刊点评 投稿经验总结 SCIENCEGARD IMPACTFACTOR 派博系数 清华大学 Yale Uni. Stanford Uni.
|Archiver|手机版|小黑屋| 派博传思国际 ( 京公网安备110108008328) GMT+8, 2025-5-25 02:13
Copyright © 2001-2015 派博传思   京公网安备110108008328 版权所有 All rights reserved
快速回复 返回顶部 返回列表