Exploring Geometry: (Textbooks in Mathematics)

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

Table of Contents:
Geometry and the Axiomatic Method Early Origins of Geometry Thales and Pythagoras Project 1 - The Ratio Made of Gold The Rise of the Axiomatic Method Properties of the Axiomatic Systems Euclid's Axiomatic Geometry Project 2 - A Concrete Axiomatic System Euclidean Geometry Angles, Lines, and Parallels ANGLES, LINES, AND PARALLELS 51 Congruent Triangles and Pasch's Axiom Project 3 - Special Points of a Triangle Measurement and Area Similar Triangles Circle Geometry Project 4 - Circle Inversion and Orthogonality Analytic Geometry The Cartesian Coordinate System Vector Geometry Project 5 - Bezier Curves Angles in Coordinate Geometry The Complex Plane Birkhoff's Axiomatic System Constructions Euclidean Constructions Project 6 - Euclidean Eggs Constructibility Transformational Geometry Euclidean Isometries Reflections Translations Rotations Project 7 - Quilts and Transformations Glide Reflections Structure and Representation of Isometries Project 8 - Constructing Compositions Symmetry Finite Plane Symmetry Groups Frieze Groups Wallpaper Groups Tilting the Plane Project 9 - Constructing Tesselations Hyperbollic Geometry Background and History Models of Hyperbolic Geometry Basic Results in Hyperbolic Geometry Project 10 - The Saccheri Quadrilateral Lambert Quadrilaterals and Triangles Area in Hyperbolic Geometry Project 11 - Tilting the Hyperbolic Plane Elliptic Geometry Background and History Perpendiculars and Poles in Elliptic Geometry Project 12 - Models of Elliptic Geometry Basic Results in Elliptic Geometry Triangles and Area in Elliptic Geometry Project 13 - Elliptic Tiling Projective Geometry Universal Themes Project 14 - Perspective and Projection Foundations of Projective Geometry Transformations and Pappus's Theorem Models of Projective Geometry Project 15 - Ratios and Harmonics Harmonic Sets Conics and Coordinates Fractal Geometry The Search for a "Natural" Geometry Self-Similarity Similarity Dimension Project 16 - An Endlessly Beautiful Snowflake Contraction Mappings Fractal Dimension Project 17 - IFS Ferns Algorithmic Geometry Grammars and Productions Project 18 - Words Into Plants Appendix A: A Primer on Proofs Appendix A A Primer on Proofs 497 Appendix B Book I of Euclid’s Elements Appendix C Birkhoff’s Axioms Appendix D Hilbert’s Axioms Appendix E Wallpaper Groups

About the Author :
Michael Hvidsten is Professor of Mathematics at Gustavus Adlophus College in St. Peter, Minnesota. He holds a PhD from the University of Illinois. His research interests include minimal surfaces, computer graphics and scientific visualizations, and software development. Geometry Explorer software is available free from his website.