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Geometry with Geometry Explorer

Geometry with Geometry Explorer


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About the Book

Geometry with Geometry Explorer combines a discovery-based geometry text with powerful integrated geometry software. This combination allows for the deep exploration of topics that would be impossible without well-integrated technology, 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.

Table of Contents:
1 Geometry and the Axiomatic Method1.1 Early Origins of Geometry1.2 Thales and Pythagoras1.2.1 Thales1.2.2 Pythagoras1.3 Project 1 - The Ratio Made of Gold1.3.1 Golden Section1.3.2 Golden Rectangles1.4 The Rise of the Axiomatic Method1.5 Properties of Axiomatic Systems1.5.1 Consistency1.5.2 Independence1.5.3 Completeness1.5.4 Gödel's Incompleteness Theorem1.6 Euclid's Axiomatic Geometry1.6.1 Euclid's Postulates1.7 Project 2 - A Concrete Axiomatic System2 Euclidean Geometry2.1 Angles, Lines, and Parallels2.2 Congruent Triangles and Pasch's Axiom2.3 Project 3 - Special Points of a Triangle2.3.1 Circumcenter2.3.2 Orthocenter2.3.3 Incenter2.4 Measurement and Area in Eucliedean Geometry2.4.1 Mini-Project - Area in Euclidean Geometry2.4.2 Cevians and Areas2.5 Similar Triangles2.5.1 Mini-Project - Finding Heights2.6 Circle Geometry2.7 Project 4 - Circle Inversion and Orthogonality2.7.1 Orthogonal Circles Redux3 Analytic Geometry3.1 The Cartesian Coordinate System3.2 Vector Geometry3.3 Project 5 - Bézier Curves3.4 Angles in Coordinate Geometry3.5 The Complex Plane3.5.1 Polar Form3.5.2 Complex Functions3.5.3 Analytic Functions and Conformal Maps (Optional)3.6 Birkhoff's Axiomatic System for Analytic Geometry4 Constructions4.1 Euclidean Constructions4.2 Project 6 - Euclidean Eggs4.3 Constructibility4.4 Mini-Project - Origami Construction5 Transformational Geometry5.1 Euclidean Isometries5.2 Reflections5.2.1 Mini-Project - Isometries through Reflection5.2.2 Reflection and Symmetry5.3 Translations5.3.1 Translational Symmetry5.4 Rotations5.4.1 Rotational Symmetry5.5 Project 7 - Quilts and Transformations5.6 Glide Reflections5.6.1 Glide Reflection Symmetry5.7 Structure and Representation of Isometries5.7.1 Matrix Form of Isometries5.7.2 Compositions of Rotations and Translations5.7.3 Compositions of Reflections and Glide Reflections5.7.4 Isometries in Computer Graphics5.7.5 Summary of Isometry Compositions5.8 Project 8 - Constructing Compositions6 Symmetry6.1 Finite Plane Symmetry Groups6.2 Frieze Groups6.3 Wallpaper Groups6.4 Tiling the Plane6.4.1 Escher6.4.2 Regular Tessellations of the Plane6.5 Project 9 - Constructing Tessellations7 Non-Euclidean Geometry7.1 Background and History7.2 Models of Hyperbolic Geometry7.2.1 Poincaré Model7.2.2 Mini-Project - The Klein Model7.3 Basic Results in Hyperbolic Geometry7.3.1 Parallels in Hyperbolic Geometry7.3.2 Omega Points and Triangles7.4 Project 10 - The Saccheri Quadrilateral7.5 Lambert Quadrilaterals and Triangles7.5.1 Lambert Quadrilaterals7.5.2 Triangles in Hyperbolic Geometry7.6 Area in Hyperbolic Geometry7.7 Project 11 - Tiling the Hyperbolic Plane7.8 Models and Isomorphism8 Non-Euclidean Transformations8.1 Möbius Transformations8.1.1 Fixed Points and the Cross Ratio8.1.2 Geometric Properties of Möbius Transformations8.2 Isometries in the Poincaré Model8.3 Isometries in the Klein Model8.4 Mini-Project - The Upper Half-Plane Model8.5 Weierstrass Model8.6 Hyperbolic Calculation8.6.1 Arclength of Parameterized Curves8.6.2 Geodesics8.6.3 The Angle of Parallelism8.6.4 Right Triangles8.6.5 Area8.7 Project 12 - Infinite Real Estate?9 Fractal Geometry9.1 The Search for a "Natural" Geometry9.2 Self-Similarity9.2.1 Sierpinski's Triangle9.2.2 Cantor Set9.3 Similarity Dimension9.4 Project 13 - An Endlessly Beautiful Snowflake9.5 Contraction Mappings and the Space of Fractals9.6 Fractal Dimension9.7 Project 14 - IFS Ferns9.8 Algorithmic Geometry9.8.1 Turtle Geometry9.9 Grammars and Productions9.9.1 Space-filling Curves9.10 Project 15 - Words into Plants: The Geometry of LifeA Book I of Euclid's ElementsA.1 DefinitionsA.2 The Postulates (Axioms)A.3 Common NotionsA.4 Propositions (Theorems)B Brief Guide to Geometry ExplorerB.1 The Main Geometry Explorer WindowB.2 Selecting ObjectsB.3 Active vs. Inactive ToolsB.4 LabelsB.5 Object ColoringB.6 Online HelpB.7 Undo/Redo of ActionsB.8 Clearing and Resizing the CanvasB.9 Saving Files as ImagesB.10 Main Window Button PanelsB.10.1 Create PanelB.10.2 Construct PanelB.10.3 Transform PanelB.11 Measurement in Geometry ExplorerB.11.1 Neutral MeasurementsB.11.2 Euclidean-only MeasurementsB.11.3 Hyperbolic-only MeasurementsB.11.4 User Input MeasurementsB.12 Using TablesB.13 Using the CalculatorB.14 Hyperbolic GeometryB.15 Analytic GeometryB.16 Turtle GeometryC Birkhoff's Axioms for Euclidean GeometryD Hilbert's Axioms for Euclidean GeometryE The 17 Wallpaper Groups


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Product Details
  • ISBN-13: 9780073129907
  • Publisher: McGraw-Hill Education - Europe
  • Publisher Imprint: McGraw-Hill Professional
  • Height: 241 mm
  • Returnable: N
  • Weight: 762 gr
  • ISBN-10: 0073129909
  • Publisher Date: 16 Jan 2005
  • Binding: Book
  • Language: English
  • Spine Width: 28 mm
  • Width: 163 mm


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Geometry with Geometry Explorer
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