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Exploring Geometry: Textbooks in Mathematics

Autor Michael Hvidsten
en Limba Engleză Hardback – 5 dec 2016
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
  • Citește tot Restrânge

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    Specificații

    ISBN-13: 9781498760805
    ISBN-10: 1498760805
    Pagini: 558
    Ilustrații: 4 Tables, black and white; 557 Illustrations, black and white
    Dimensiuni: 156 x 234 x 34 mm
    Greutate: 1.12 kg
    Ediția:2 New edition
    Editura: CRC Press
    Colecția Chapman and Hall/CRC
    Seria Textbooks in Mathematics


    Public țintă

    Academic

    Cuprins

    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

    Notă biografică

    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.

    Descriere

    This text 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.