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New Horizons in Geometry

New Horizons in Geometry

$65.99 (P)

Part of Dolciani Mathematical Expositions

  • Date Published: March 2013
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9780883853542

$ 65.99 (P)
Hardback

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About the Authors
  • The collaborative work of Tom Apostol and Mamikon Mnatsakanian has been lauded for its clarity and originality. In this volume the authors present an impressive collection of geometric results that reveal surprising connections between lengths, areas and volumes in various shapes, and allow one to compute difficult integrals, all using intuitive visual calculations. One noteworthy idea that the reader will encounter is Mamikon's Sweeping Tangent Theorem from which the authors obtain a visual derivation of the property that the length of an arc of a catenary is proportional to the area under the arc. This is one of many 'proofs without words' contained within. In addition, a variety of results are derived visually for cycloids, conic sections, and many more geometric objects. As befits a book that emphasises visual thinking, the text is beautifully illustrated. This is a book that will inspire students and enrich any geometry or calculus course.

    • A striking and original new approach to geometry and calculus
    • Emphasises dynamic visual thinking
    • Beautifully illustrated throughout
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    Product details

    • Date Published: March 2013
    • format: Hardback
    • isbn: 9780883853542
    • length: 526 pages
    • dimensions: 262 x 187 x 37 mm
    • weight: 1.6kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    1. Mamikon's sweeping tangent theorem
    2. Cycloids and trochoids
    3. Cyclogons and trochogons
    4. Circumgons and circumsolids
    5. The method of punctured containers
    6. Unwrapping curves from cylinders and cones
    7. New descriptions of conics via twisted cylinders, focal disks, and directors
    8. Ellipse to hyperbola: 'with this string I thee wed'
    9. Trammels
    10. Isoperimetric and isoparametric problems
    11. Arclength and tanvolutes
    12. Centroids
    13. Sums of squares
    14. Appendix.

  • Authors

    Tom M. Apostol, California Institute of Technology
    Tom Apostol is an Emeritus Professor of Mathematics at the California Institute of Technology.

    Mamikon A. Mnatsakanian, California Institute of Technology
    Mamikon Mnatsakanian is Project Associate at 'Project Mathematics!' at the California Institute of Technology.

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