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Experiencing Geometry, 3/E
David W. Henderson, Cornell University
Daina Taimina, Cornell University

ISBN-10: 0131437488
ISBN-13:  9780131437487

Publisher:  Pearson
Copyright:  2005
Format:  Paper; 432 pp
Published:  07/28/2004
Status: Instock


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Description

For junior/senior level course in Geometry.

The distinctive approach of Henderson and Taimina's text stimulates students to develop a broader, deeper understanding of mathematics through active experience—including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting problems (ranging from easy to challenging) encourage students to gather and discuss their reasonings and understanding. This is the only undergraduate text that pays attention to geometric intuition, student cognitive development, and rigorous mathematics; and that includes a broad vision of geometry that leads to discussion of four strands in the history of geometry and to an understanding of the possible shapes of the physical universe.


Features

  • NEW - Co-author Daina Taimina brings unique experience and knowledge to third edition.

    • Provides students with the benefit of her considerable experience with and knowledge of the history of mathematics, as well as the benefits of more than 25 years of experience teaching geometry.

  • NEW - Historical Development of Geometry added—Provides a foundation for understanding four practical causes of the evolution of geometry, and uses the framework of these strands to infuse history in to each chapter.

    • Enhances students understanding of geometry and clears up many misconceptions.

  • NEW - Reorganized and revised with new chapters and material—Circles in the Plane chapter split into Projections of a Sphere onto a Plane and Circles with added material about circles on spheres and hyperbolic plane and about involutes on all three surfaces.

    • Provides students with a more reasonable presentation with more information on circles, spheres, hyperbolic planes and about involutes on all three surfaces.

  • NEW - Inversions in circles material added—i.e. Material on spheres and hyperbolic plane.

    • Provides students with more information on this important topic.

  • NEW - Geometry of Mechanisms chapter added.

    • Provides students with information on historical machines and modern results related to robotics.

  • NEW - Shape of space discussion updated to reflect recent discoveries—Introduces the geometry needed to understand the possibilities for the shape of the physical universe.

    • Provides students with the most up-to-date discoveries and theories regarding the possible shape of the physical universe and allows them to appreciate the results of the new and forthcoming space observations.

  • Integration of hyperbolic and spherical geometry with the Euclidean geometry—Every geometric notion is explored in relation to the Euclidean plane, on spheres and on hyperbolic planes.

    • Allows students to learn new geometries and gain a better understanding of basic notions of Euclidean geometry.

  • Concrete models to introduce and explore spherical geometry and hyperbolic geometry—Provides a unique approach to learning hyperbolic geometry through the use of hyperbolic surfaces.

    • Provides students with a concrete, intuitive introduction to hyperbolic geometry that gives meaning to usually abstract presentations.

  • Geometric manifold introduction—Covers both two-dimensional and three-dimensional geometric manifold.

    • Exposes students to the basic idea of “manifold,” which has application in physics, engineering, biology and cosmology.

  • Stand-alone chapters with minimum core—Majority of chapters are independent of each other.

    • Allows instructors to present the majority of the chapters in any order after the minimum core has been covered.

  • Problem based—Reflects recent NCTM and NRC standards for student-centered, activity-center texts. More than 100 multi-part problems lead students to explore and experience the geometric notions presented.

    • Allows students to experience modern and classical meanings and concepts of geometry and gain experience with what it means to do mathematics through the use of multi-part, open-ended problems.

  • Distinction between intrinsic and extrinsic, and local and global.

    • Provides students with a modern and alive approach that applies to other aspects of mathematics and of their lives.

  • Parallel transport—Introduced early and used throughout the text.

    • Introduces students to a powerful and easily understood notion that has practical applications in multiple disciplines.

  • Writing encouraged—Problems can easily be used as writing assignments.

    • Provides students with opportunities to improve their writing skills in mathematics and through it to gain deeper understandings.

  • Instructor's Manual—A webpage containing updates on recent results and discoveries, useful web links, expanded annotated bibliography, and additional information.


New To This Edition

  • Co-author Daina Taimina brings unique experience and knowledge to third edition.

    • Provides students with the benefit of her considerable experience with and knowledge of the history of mathematics, as well as the benefits of more than 25 years of experience teaching geometry.

  • Historical Development of Geometry added—Provides a foundation for understanding four practical causes of the evolution of geometry, and uses the framework of these strands to infuse history in to each chapter.

    • Enhances students understanding of geometry and clears up many misconceptions.

  • Reorganized and revised with new chapters and material—Circles in the Plane chapter split into Projections of a Sphere onto a Plane and Circles with added material about circles on spheres and hyperbolic plane and about involutes on all three surfaces.

    • Provides students with a more reasonable presentation with more information on circles, spheres, hyperbolic planes and about involutes on all three surfaces.

  • Inversions in circles material added—i.e. Material on spheres and hyperbolic plane.

    • Provides students with more information on this important topic.

  • Geometry of Mechanisms chapter added.

    • Provides students with information on historical machines and modern results related to robotics.

  • Shape of space discussion updated to reflect recent discoveries—Introduces the geometry needed to understand the possibilities for the shape of the physical universe.

    • Provides students with the most up-to-date discoveries and theories regarding the possible shape of the physical universe and allows them to appreciate the results of the new and forthcoming space observations.


Table of Contents



Preface.


How to Use this Book.


 0. Historical Strands of Geometry.


 1. What is Straight?


 2. Straightness on Spheres.


 3. What Is an Angle?


 4. Straightness on Cylinders and Cones.


 5. Straightness on Hyperbolic Planes.


 6. Triangles and Congruencies.


 7. Area and Holonomy.


 8. Parallel Transport.


 9. SSS, ASS, SAA, and AAA.


10. Parallel Postulates.


11. Isometries and Patterns.


12. Dissection Theory.


13. Square Roots, Pythagoras and Similar Triangles.


14. Projections of a Sphere onto a Plane.


15. Circles.


16. Inversions in Circles.


17. Projections (Models) of Hyperbolic Planes.


18. Geometric 2-Manifolds.


19. Geometric Solutions of Quadratic and Cubic Equations.


20. Trigonometry and Duality.


21. Mechanisms.


22. 3-Spheres and Hyperbolic 3-Spaces.


23. Polyhedra.


24. 3-Manifolds—the Shape of Space.


Appendix A: Euclid's Definitions, Postulates, and Common Notions.


Appendix B: Constructions of Hyperbolic Planes.


Bibliography.


Index.



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Reviews

"I like the authors' writing style and I think the explanations are very clear .... I know that my students read this book, which is certainly saying something. Sometimes they think it's hard to read, but it is at least possible-and they could think it's hard to read because it might be one of the few times they have actually had to read the text .... I think the historical illustrations will be useful for creating interest with the students. This is a nice addition to this edition of the text." — Barbara Edwards, Oregon State University

"I found this text to be a wonderful, fresh, and innovative treatment of geometry. The Moore method of study by doing and involving the student works very well indeed for this subject. The style of the text is very friendly and encouraging and gets the student involved quickly with a give-and-take approach. The student develops insights and skills probably not obtainable in more traditional courses. This is a very fine text that I would strongly recommend for a beginning course in Euclidean and non-Euclidean geometry." — Norman Johnson, University of Iowa

"This book remains a treasure, an essential reference. I simply know of no other book that attempts the broad vision of geometry that this book does, that does it by-and-large so successfully, and that pays so much attention to geometric intuition, student cognitive development, and rigorous mathematics." — Judy Roitman, University of Kansas

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