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New Horizons in Geometry, Tom M. Apostol, Mamikon A Mnatsakanian

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About this book :-
New Horizons in Geometry written by Tom M. Apostol, Mamikon A Mnatsakanian .
This book is a compendium of joint work produced by the authors during the period 1998–2012, most of it published in the American Mathematical Monthly, Math Horizons, Mathematics Magazine, and The Mathematical Gazette. The published papers have been edited, augmented, and rearranged into 15 chapters. Each chapter is preceded by a sample of problems that can be solved by the methods developed in that chapter. Each opening page contains a brief abstract of the chapter’s contents.
New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order.
The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry
(Tom M. Apostol, Mamikon A Mnatsakanian)

Book Detail :-
Title: New Horizons in Geometry
Edition:
Author(s): Tom M. Apostol, Mamikon A Mnatsakanian
Publisher: The Mathematical Association of America
Series: Dolciani mathematical expositions no. 47
Year: 2012
Pages: 528
Type: PDF
Language: English
ISBN: 088385354X,978-0-88385-354-2,978-1-61444-210-3,161444210X
Country: US
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About Author :- The author Tom M. Apostol joined the Caltech faculty in 1950 and is Professor of Mathematics, Emeritus. He is internationally known for his books on Calculus, Analysis, and Analytic Number Theory, (translated into 7 languages), and for creating Project MATHEMATICS!, a video series that brings mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international festivals, and were translated into Hebrew, Portuguese, French, and Spanish. Apostol has published 102 research papers, has written two chapters for the Digital Library of Mathematical Functions (2010), and is coauthor of three texts for the physics telecourse.
He has received several awards for research and teaching. In 1978 he was a visiting professor at the University of Patras, Greece, and in 2001 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. In 2012 he was selected to be a Fellow of the American Mathematical Society.

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Book Contents :-
New Horizons in Geometry written by Tom M. Apostol, Mamikon A Mnatsakanian cover the following topics. '
Introduction
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. New Balancing Principles with Applications
14. Sums of Squares
15. Appendix
Bibliography
Index

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