Skip to content
Register Sign in Wishlist
New Horizons in Geometry

New Horizons in Geometry


Part of Dolciani Mathematical Expositions

  • Date Published: March 2013
  • availability: Out of stock in print form with no current plan to reprint
  • format: Hardback
  • isbn: 9780883853542

£ 46.99

Out of stock in print form with no current plan to reprint
Unavailable Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
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
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: March 2013
    • format: Hardback
    • isbn: 9780883853542
    • length: 526 pages
    • dimensions: 262 x 187 x 37 mm
    • weight: 1.6kg
    • availability: Out of stock in print form with no current plan to reprint
  • 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.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.