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Exploring Geometry: Textbooks in Mathematics

Autor Michael Hvidsten
en Limba Engleză Paperback – 21 ian 2023
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
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    Specificații

    ISBN-13: 9781032477060
    ISBN-10: 1032477067
    Pagini: 558
    Ilustrații: 557
    Dimensiuni: 156 x 234 mm
    Greutate: 1.03 kg
    Ediția:2
    Editura: CRC Press
    Colecția CRC Press
    Seria Textbooks in Mathematics


    Public țintă

    Academic

    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.

    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

    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 h