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Geometry Illuminated

Geometry Illuminated
An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry


Part of Mathematical Association of America Textbooks

  • Date Published: September 2015
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9781939512116

£ 45.99

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About the Authors
  • An introduction to geometry in the plane, both Euclidean and hyperbolic, this book is designed for an undergraduate course in geometry. With its patient approach, and plentiful illustrations, it will also be a stimulating read for anyone comfortable with the language of mathematical proof. While the material within is classical, it brings together topics that are not generally found together in books at this level, such as: parametric equations for the pseudosphere and its geodesics; trilinear and barycentric coordinates; Euclidean and hyperbolic tilings; and theorems proved using inversion. The book is divided into four parts, and begins by developing neutral geometry in the spirit of Hilbert, leading to the Saccheri–Legendre Theorem. Subsequent sections explore classical Euclidean geometry, with an emphasis on concurrence results, followed by transformations in the Euclidean plane, and the geometry of the Poincaré disk model.

    • Emphasises the logical development of geometries within an axiomatic system
    • Brings together a distinctive selection of topics that are not often found together in books at this level
    • Extensively illustrated to enhance the reader's journey
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    Product details

    • Date Published: September 2015
    • format: Hardback
    • isbn: 9781939512116
    • length: 558 pages
    • dimensions: 262 x 185 x 32 mm
    • weight: 1.15kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    Axioms and models
    Part I. Neutral Geometry:
    1. The axioms of incidence and order
    2. Angles and triangles
    3. Congruence verse I: SAS and ASA
    4. Congruence verse II: AAS
    5. Congruence verse III: SSS
    6. Distance, length and the axioms of continuity
    7. Angle measure
    8. Triangles in neutral geometry
    9. Polygons
    10. Quadrilateral congruence theorems
    Part II. Euclidean Geometry:
    11. The axiom on parallels
    12. Parallel projection
    13. Similarity
    14. Circles
    15. Circumference
    16. Euclidean constructions
    17. Concurrence I
    18. Concurrence II
    19. Concurrence III
    20. Trilinear coordinates
    Part III. Euclidean Transformations:
    21. Analytic geometry
    22. Isometries
    23. Reflections
    24. Translations and rotations
    25. Orientation
    26. Glide reflections
    27. Change of coordinates
    28. Dilation
    29. Applications of transformations
    30. Area I
    31. Area II
    32. Barycentric coordinates
    33. Inversion I
    34. Inversion II
    35. Applications of inversion
    Part IV. Hyperbolic Geometry:
    36. The search for a rectangle
    37. Non-Euclidean parallels
    38. The pseudosphere
    39. Geodesics on the pseudosphere
    40. The upper half-plane
    41. The Poincaré disk
    42. Hyperbolic reflections
    43. Orientation preserving hyperbolic isometries
    44. The six hyperbolic trigonometric functions
    45. Hyperbolic trigonometry
    46. Hyperbolic area
    47. Tiling

  • Author

    Matthew Harvey, University of Virginia
    Matthew Harvey is an Associate Professor of Mathematics at the University of Virginia's College at Wise, where he has taught since 2006. He graduated from the University of Virginia in 1995 with a BA in Mathematics, and from Johns Hopkins University in 2002 with a PhD in Mathematics.

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