a Course of Plane Geometry
Impreso
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This book presents plane geometry following Hilbert\'s axiomatic system. It is inspired on R. Hartshome\'s fantastic book Geometry: Euclid and  Beyond, and can be considered as a careful exposition of most of chapter II of that book. 
 
It must be remarked that non-euclidean geometries, i.e. geometries not satisfying the fifth postulate of Euclid, enter the scene, in a natural way, from the very beginning. 
 
The vast majority of plane geometry texts are only concerned with euclidean geometry, loosing the oportunity of not only teaching rigorous reasoning to freshmen, but at the same time exposing them to the mind expanding experience of contemplating the strange geometries conceived, in the first decades of the XIX century, by Gauss, Lobachevsky and Bolyai. 
[short_description] =>
This book presents plane geometry following Hilbert\'s axiomatic system. It is inspired on R. Hartshome\'s fantastic book Geometry: Euclid and  Beyond, and can be considered as a careful exposition of most of chapter II of that book. 
 
It must be remarked that non-euclidean geometries, i.e. geometries not satisfying the fifth postulate of Euclid, enter the scene, in a natural way, from the very beginning. 
 
The vast majority of plane geometry texts are only concerned with euclidean geometry, loosing the oportunity of not only teaching rigorous reasoning to freshmen, but at the same time exposing them to the mind expanding experience of contemplating the strange geometries conceived, in the first decades of the XIX century, by Gauss, Lobachevsky and Bolyai. 
[products_toc] =>

Contents 
Preface 

Acknowledgments 

1 Introduction 
1.1 A Short History of Geometry
1.2 What you will and will not learn in this book 
1.3 Audience prerequisites and style of explanation
1.4 Book plan 
1.5 How to study this book  

2 Preliminaries 
2.1 Proof methods  
2.1.1 Methods for proving conditional statements 
2.1.2 Methods for proving other types of statements 
2.1.3 Symbolic representation 
2.1.4 More examples of proofs 
2.1.5 Exercises
2.2 Elementary theory of sets 
2.2.1 Set operations 
2.2.2 Relations 
2.2.3 Equivalence relations
 

3 Incidence geometry 
3.1 The notion of incidence geometry 
3.2 Lines and collinearity  
3.3 Examples of incidence geometries 
3.3.1 Some basic examples of incidence geometries 
3.3.2 The main incidence geometries 
3.3.3 Generalizing the real cartesian plane  
3.4 Parallelism
3.5 Behavior of parallelism in our examples 

4 Betweenness 
4.1 Betweenness structures, segments, triangles, and convexity  
4.2 Separation of the plane by a line 
4.3 Separation of a line by one of its points 
4.4 Rays 
4.5 Angles 
4.6 Betweenness structure for the real cartesian plane 
4.7 Betweenness structure for the hyperbolic plane  

5 Congruence of segments 
5.1 Congruence of segments structure and segment comparison  
5.2 The usual congruence of segments structure for the real cartesian plane
5.3 The usual congruence of segments structure for the hyperbolic plane  
 
6 Congruence of angles 
6.1 Congruence of angles structure and angle comparison 
6.2 Angle congruence in our main examples
6.2.1 Congruence of angles in the real cartesian plane 
6.2.2 Congruence of angles in the hyperbolic plane  

7 Hilbert planes 
7.1 Circ1es 
7.2 Book 1 of The Elements 

References 

Index 




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a Course of Plane Geometry

$50.000
$42.500

Este libro se encuentra en la modalidad Impreso, el tiempo de entrega tarda de 3 a 7 días hábiles después de su adquisición.

This book presents plane geometry following Hilbert\'s axiomatic system. It is inspired on R. Hartshome\'s fantastic book Geometry: Euclid and  Beyond, and can be considered as a careful exposition of most of chapter II of that book. 
 
It must be remarked that non-euclidean geometries, i.e. geometries not satisfying the fifth postulate of Euclid, enter the scene, in a natural way, from the very beginning. 
 
The vast majority of plane geometry texts are only concerned with euclidean geometry, loosing the oportunity of not only teaching rigorous reasoning to freshmen, but at the same time exposing them to the mind expanding experience of contemplating the strange geometries conceived, in the first decades of the XIX century, by Gauss, Lobachevsky and Bolyai. 

Tabla de Contenido


Contents 
Preface 

Acknowledgments 

1 Introduction 
1.1 A Short History of Geometry
1.2 What you will and will not learn in this book 
1.3 Audience prerequisites and style of explanation
1.4 Book plan 
1.5 How to study this book  

2 Preliminaries 
2.1 Proof methods  
2.1.1 Methods for proving conditional statements 
2.1.2 Methods for proving other types of statements 
2.1.3 Symbolic representation 
2.1.4 More examples of proofs 
2.1.5 Exercises
2.2 Elementary theory of sets 
2.2.1 Set operations 
2.2.2 Relations 
2.2.3 Equivalence relations
 

3 Incidence geometry 
3.1 The notion of incidence geometry 
3.2 Lines and collinearity  
3.3 Examples of incidence geometries 
3.3.1 Some basic examples of incidence geometries 
3.3.2 The main incidence geometries 
3.3.3 Generalizing the real cartesian plane  
3.4 Parallelism
3.5 Behavior of parallelism in our examples 

4 Betweenness 
4.1 Betweenness structures, segments, triangles, and convexity  
4.2 Separation of the plane by a line 
4.3 Separation of a line by one of its points 
4.4 Rays 
4.5 Angles 
4.6 Betweenness structure for the real cartesian plane 
4.7 Betweenness structure for the hyperbolic plane  

5 Congruence of segments 
5.1 Congruence of segments structure and segment comparison  
5.2 The usual congruence of segments structure for the real cartesian plane
5.3 The usual congruence of segments structure for the hyperbolic plane  
 
6 Congruence of angles 
6.1 Congruence of angles structure and angle comparison 
6.2 Angle congruence in our main examples
6.2.1 Congruence of angles in the real cartesian plane 
6.2.2 Congruence of angles in the hyperbolic plane  

7 Hilbert planes 
7.1 Circ1es 
7.2 Book 1 of The Elements 

References 

Index