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New horizons in geometry / Tom M. Apostol, California Institute of Technology and Mamikon A. Mnatsakanian, California Institute of Technology.

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Author/Creator:
Apostol, Tom M., author.
Language:
English.
Publication date:
2012
Copyright date:
2012
Publication:
Washington, DC : The Mathematical Association of America, [2012]
Distribution:
Mathematical Association of America
Manufacture:
South Korea ; Pasadena, CA : Charles Allen Imaging Experts
Copyright notice:
©2012
Format:
  • Book
  • xiv, 513 pages : color illustrations ; 27 cm.
Bibliography:
Includes bibliographical references (pages 501-504) and index.
Contents:
  • Ch. 1. Mamikon's sweeping
  • tangent theorem
  • Ch. 2. Cycloids and trochoids
  • Ch. 3. Cyclogons and trochogons
  • Ch. 4. Circumgons and circumsolids
  • Ch. 5. The method of punctured containers
  • Ch. 6. Unwrapping curves from cylinders and cones
  • Ch. 7. New descriptions of conics via twisted cylinders, focal disks, and directors
  • Ch. 8. Ellipse to hyperbola: with this string I thee wed
  • Ch. 9. Trammels
  • Ch. 10. Isoperimetric and isoparametric problems
  • Ch. 11. Arclength and tanvolutes
  • Ch. 12. Centroids
  • Ch. 13. New balancing principles with applications
  • Ch. 14. Sums of squares.
Summary:
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.
Contributor:
Mnatsakanian, Mamikon A., author, illustrator.
Series:
The Dolciani mathematical expositions ; number 47
Dolciani mathematical expositions ; no. 47.
Subjects:
ISBN:
9780883853542
088385354X
9781614442103

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