New horizons in geometry
- Responsibility
- Tom M. Apostol, California Institute of Technology and Mamikon A. Mnatsakanian, California Institute of Technology.
- Language
- English.
- 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
- Physical description
- xiv, 513 pages : color illustrations ; 27 cm.
- Series
- Dolciani mathematical expositions ; no. 47.
Access
Available online
Math & Statistics Library
Stacks
| Call number | Status |
|---|---|
| QA445 .A66 2012 |
More options
Creators/Contributors
- Author/Creator
- Apostol, Tom M., author.
- Contributor
- Mnatsakanian, Mamikon A., author, illustrator.
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 501-504) and index.
- 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.
- (source: Nielsen Book Data)9780883853542 20160612
- Publisher's 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.
(source: Nielsen Book Data)9780883853542 20160612
Bibliographic information
- Publication date
- 2012
- Copyright date
- 2012
- Series
- The Dolciani mathematical expositions ; number 47
- ISBN
- 9780883853542 (pbk.)
- 088385354X (pbk.)
- 9781614442103 (ebk.)
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