Hvidsten, Michael  <br/><br/>
Geometry with geometry explorer / 
Michael Hvidsten. 
 - Dubuque, Iowa :   McGraw-Hill,   c2005. 
 - xiii, 463 pages :  illustrations ;   24 cm + 1   CD-ROM (4 3/4 in.) 
<br/><br/>Includes bibliographical references (p. 453-456) and index. 
<br/><br/>Includes bibliographical references. 
<br/><br/>1 Geometry and the Axiomatic Method 1.1 Early Origins of Geometry 1.2 Thales and Pythagoras<br/>1.2.1 Thales<br/>1.2.2 Pythagoras 1.3 Project 1 - The Ratio Made of Gold<br/>1.3.1 Golden Section<br/>1.3.2 Golden Rectangles 1.4 The Rise of the Axiomatic Method 1.5 Properties of Axiomatic Systems<br/>1.5.1 Consistency<br/>1.5.2 Independence<br/>1.5.3 Completeness<br/>1.5.4 Gödel's Incompleteness Theorem 1.6 Euclid's Axiomatic Geometry<br/>1.6.1 Euclid's Postulates 1.7 Project 2 - A Concrete Axiomatic System 2 Euclidean Geometry 2.1 Angles, Lines, and Parallels 2.2 Congruent Triangles and Pasch's Axiom 2.3 Project 3 - Special Points of a Triangle<br/>2.3.1 Circumcenter<br/>2.3.2 Orthocenter<br/>2.3.3 Incenter 2.4 Measurement and Area in Eucliedean Geometry<br/>2.4.1 Mini-Project - Area in Euclidean Geometry<br/>2.4.2 Cevians and Areas 2.5 Similar Triangles<br/>2.5.1 Mini-Project - Finding Heights 2.6 Circle Geometry 2.7 Project 4 - Circle Inversion and Orthogonality<br/>2.7.1 Orthogonal Circles Redux 3 Analytic Geometry 3.1 The Cartesian Coordinate System 3.2 Vector Geometry 3.3 Project 5 - Be;zier Curves 3.4 Angles in Coordinate Geometry 3.5 The Complex Plane<br/>3.5.1 Polar Form<br/>3.5.2 Complex Functions<br/>3.5.3 Analytic Functions and Conformal Maps (Optional) 3.6 Birkhoff's Axiomatic System for Analytic Geometry 4 Constructions 4.1 Euclidean Constructions 4.2 Project 6 - Euclidean Eggs 4.3 Constructibility 4.4 Mini-Project - Origami Construction 5 Transformational Geometry 5.1 Euclidean Isometries 5.2 Reflections<br/>5.2.1 Mini-Project - Isometries through Reflection<br/>5.2.2 Reflection and Symmetry 5.3 Translations<br/>5.3.1 Translational Symmetry 5.4 Rotations<br/>5.4.1 Rotational Symmetry 5.5 Project 7 - Quilts and Transformations 5.6 Glide Reflections<br/>5.6.1 Glide Reflection Symmetry 5.7 Structure and Representation of Isometries<br/>5.7.1 Matrix Form of Isometries<br/>5.7.2 Compositions of Rotations and Translations<br/>5.7.3 Compositions of Reflections and Glide Reflections<br/>5.7.4 Isometries in Computer Graphics<br/>5.7.5 Summary of Isometry Compositions 5.8 Project 8 - Constructing Compositions 6 Symmetry 6.1 Finite Plane Symmetry Groups 6.2 Frieze Groups 6.3 Wallpaper Groups 6.4 Tiling the Plane<br/>6.4.1 Escher<br/>6.4.2 Regular Tessellations of the Plane 6.5 Project 9 - Constructing Tessellations 7 Non-Euclidean Geometry 7.1 Background and History 7.2 Models of Hyperbolic Geometry<br/>7.2.1 Poincare; Model<br/>7.2.2 Mini-Project - The Klein Model 7.3 Basic Results in Hyperbolic Geometry<br/>7.3.1 Parallels in Hyperbolic Geometry<br/>7.3.2 Omega Points and Triangles 7.4 Project 10 - The Saccheri Quadrilateral 7.5 Lambert Quadrilaterals and Triangles<br/>7.5.1 Lambert Quadrilaterals<br/>7.5.2 Triangles in Hyperbolic Geometry 7.6 Area in Hyperbolic Geometry 7.7 Project 11 - Tiling the Hyperbolic Plane 7.8 Models and Isomorphism 8 Non-Euclidean Transformations 8.1 Möbius Transformations<br/>8.1.1 Fixed Points and the Cross Ratio<br/>8.1.2 Geometric Properties of Möbius Transformations 8.2 Isometries in the Poincare; Model 8.3 Isometries in the Klein Model 8.4 Mini-Project - The Upper Half-Plane Model 8.5 Weierstrass Model 8.6 Hyperbolic Calculation<br/>8.6.1 Arclength of Parameterized Curves<br/>8.6.2 Geodesics<br/>8.6.3 The Angle of Parallelism<br/>8.6.4 Right Triangles<br/>8.6.5 Area 8.7 Project 12 - Infinite Real Estate? 9 Fractal Geometry 9.1 The Search for a "Natural" Geometry 9.2 Self-Similarity<br/>9.2.1 Sierpinski's Triangle<br/>9.2.2 Cantor Set 9.3 Similarity Dimension 9.4 Project 13 - An Endlessly Beautiful Snowflake 9.5 Contraction Mappings and the Space of Fractals 9.6 Fractal Dimension 9.7 Project 14 - IFS Ferns 9.8 Algorithmic Geometry<br/>9.8.1 Turtle Geometry 9.9 Grammars and Productions<br/>9.9.1 Space-filling Curves 9.10 Project 15 - Words into Plants: The Geometry of Life A Book I of Euclid's Elements A.1 Definitions A.2 The Postulates (Axioms) A.3 Common Notions A.4 Propositions (Theorems) B Brief Guide to Geometry Explorer B.1 The Main Geometry Explorer Window B.2 Selecting Objects B.3 Active vs. Inactive Tools B.4 Labels B.5 Object Coloring B.6 Online Help B.7 Undo/Redo of Actions B.8 Clearing and Resizing the Canvas B.9 Saving Files as Images B.10 Main Window Button Panels<br/>B.10.1 Create Panel<br/>B.10.2 Construct Panel<br/>B.10.3 Transform Panel B.11 Measurement in Geometry Explorer<br/>B.11.1 Neutral Measurements<br/>B.11.2 Euclidean-only Measurements<br/>B.11.3 Hyperbolic-only Measurements<br/>B.11.4 User Input Measurements B.12 Using Tables B.13 Using the Calculator B.14 Hyperbolic Geometry B.15 Analytic Geometry B.16 Turtle Geometry C Birkhoff's Axioms for Euclidean Geometry D Hilbert's Axioms for Euclidean Geometry E The 17 Wallpaper Groups  
<br/><br/> Explores topics such as hyperbolic geometry, and encourages the kind of experimentation and self-discovery needed for students to develop a natural intuition for various topics in geometry. This book combines a discovery-based geometry text with integrated geometry software. 
<br/><br/><br/>In English text. 
<br/><br/><label>ISBN: </label>007124865X (paperback) 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Geometry.<br/>Geometry Explorer (Computer file).
<br/><br/><label>LC Class. No.: </label>CIR QA 445  / H84 2005