Exploring Geometry

Michael Hvidsten

• Verlag: Chapman and Hall/CRC
• Jahr: 2016
• ISBN:
  9781498760980
• Auflage: 2
• Thema: Mathematics
• Thema: Mathematics General

Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.

Features:

• Second edition of a successful textbook for the first undergraduate course
• Every major concept is introduced in its historical context and connects the idea with real life
• Focuses on experimentation
• Projects help enhance student learning
• All major software programs can be used; free software from author

Inhaltsverzeichnis

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Preface to the Second Edition
• Acknowledgments
• CHAPTER 1 Geometry and the Axiomatic Method
• CHAPTER 2 Euclidean Geometry
• CHAPTER 3 Analytic Geometry
• CHAPTER 4 Constructions
• CHAPTER 5 Transformational Geometry
• CHAPTER 6 Symmetry
• CHAPTER 7 Hyperbolic Geometry
• CHAPTER 8 Elliptic Geometry
• CHAPTER 9 Projective Geometry
• CHAPTER 10 Fractal Geometry
• APPENDIX A A Primer on Proofs
• APPENDIX B Book I of Euclid’s Elements
• APPENDIX C Birkhoff’s Axioms
• APPENDIX D Hilbert’s Axioms
• APPENDIX E Wallpaper Groups
• References
• Index