Geometry from Euclid to Knots Format: Paperback
Stahl, Saul
ISBN 10: 0486474593 ISBN 13: 9780486474595
Editore: Dover Publishers, 2010
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Brand New. Codice articolo 9780486474595
Riassunto:
Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's statements with appropriate historical commentary and many exercises &; more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems.
In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.
In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.
Contenuti: Preface to the Dover Edition Preface 1. Other Geometries: A Computational Introduction 2. The Neutral Geometry of the Triangle 3. Nonneutral Euclidean Geometry 4. Circles and Regular Polygons 5. Toward Projective Geometry 6. Planar Symmetries 7. Inversions 8. Symmetry in Space 9. Informal Topology 10. Graphs 11. Surfaces 12. Knots and Links Appendix A: A Brief Introduction to the Geometer's Sketchpad Appendix B: Summary of Propositions Appendix C: George D. Birkhoff's Axiomatization of Euclidean Geometry Appendix D: The University of Chicago School Mathematics Project's Geometrical Axioms Appendix E: David Hilbert's Axiomization of Euclidean Geometry Appendix F: Permutations AppendixG: Modular Arithmetic Solutions and Hints to Selected Problems Bibliography Index
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Titolo: Geometry from Euclid to Knots Format: ...
Casa editrice: Dover Publishers
Data di pubblicazione: 2010
Legatura: Brossura
Condizione: New