
New Horizons in Geometry
The Mathematical Association of America (Publisher)
Published on 14. March 2013
Book
Hardback
526 pages
978-0-88385-354-2 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Washington DC
United States
Publishing group
Cambridge University Press
Target group
College/higher education
Dimensions
Height: 262 mm
Width: 187 mm
Thickness: 37 mm
Weight
1600 gr
ISBN-13
978-0-88385-354-2 (9780883853542)
Schweitzer Classification
Persons
Author
California Institute of Technology
Tom Apostol is an Emeritus Professor of Mathematics at the California Institute of Technology.
Tom Apostol is an Emeritus Professor of Mathematics at the California Institute of Technology.
California Institute of Technology
Mamikon Mnatsakanian is Project Associate at 'Project Mathematics!' at the California Institute of Technology.
Mamikon Mnatsakanian is Project Associate at 'Project Mathematics!' at the California Institute of Technology.
Content
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.
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.