Description
New Horizons in Geometry
Dolciani Mathematical Expositions Series
Authors: Apostol Tom M., Mnatsakanian Mamikon A.
Language: EnglishSubject for New Horizons in Geometry:
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Add to cart the book of Apostol Tom M., Mnatsakanian Mamikon A.
Publication date: 03-2013
526 p. · 18.7x26.2 cm · Hardback
526 p. · 18.7x26.2 cm · Hardback
Description
/li>Contents
/li>Biography
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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.
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.
Tom Apostol is an Emeritus Professor of Mathematics at the 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.
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