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| Product Code: | DOL/47 |
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| eBook ISBN: | 978-1-4704-4336-8 |
| Product Code: | DOL/47.E |
| List Price: | $79.00 |
| MAA Member Price: | $63.20 |
| AMS Member Price: | $63.20 |
| Hardcover ISBN: | 978-1-4704-4335-1 |
| eBook: ISBN: | 978-1-4704-4336-8 |
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| List Price: | $164.00 $124.50 |
| MAA Member Price: | $131.20 $99.60 |
| AMS Member Price: | $131.20 $99.60 |
| Hardcover ISBN: | 978-1-4704-4335-1 |
| Product Code: | DOL/47 |
| List Price: | $85.00 |
| MAA Member Price: | $68.00 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-4336-8 |
| Product Code: | DOL/47.E |
| List Price: | $79.00 |
| MAA Member Price: | $63.20 |
| AMS Member Price: | $63.20 |
| Hardcover ISBN: | 978-1-4704-4335-1 |
| eBook ISBN: | 978-1-4704-4336-8 |
| Product Code: | DOL/47.B |
| List Price: | $164.00 $124.50 |
| MAA Member Price: | $131.20 $99.60 |
| AMS Member Price: | $131.20 $99.60 |
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Book DetailsDolciani Mathematical ExpositionsVolume: 47; 2013; 513 ppMSC: Primary 51
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.
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Table of Contents
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Chapters
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Chapter 1. Mamikon’s Sweeping-Tangent Theorem
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Chapter 2. Cycloids and Trochoids
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Chapter 3. Cyclogons and Trochogons
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Chapter 4. Circumgons and Circumsolids
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Chapter 5. The Method of Punctured Containers
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Chapter 6. Unwrapping Curves from Cylinders and Cones
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Chapter 7. New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors
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Chapter 8. Ellipse to Hyperbola: “With This String I Thee Wed”
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Chapter 9. Trammels
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Chapter 10. Isoperimetric and Isoparametric Problems
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Chapter 11. Arclength and Tanvolutes
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Chapter 12. Centroids
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Chapter 13. New Balancing Principles with Applications
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Chapter 14. Sums of Squares
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Chapter 15. Appendix
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Additional Material
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Reviews
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In a remarkable display of mathematical versatility and imagination, the authors present us with a wealth of geometrical gems. These beautiful and often surprising results deal with a multitude of geometric forms, their interrelationships, and in many cases, their connection with patterns underlying the laws of nature.
Don Chakerian -
... The authors 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 and extensions of familiar theorems. Lengths, areas and volumes of curves, surfaces and solids are explored from a visually captivating perspective. ... The hundreds of full color illustrations are visually enticing and provide great motivation to read further and savor the wonderful results. This book is a must have for any geometer.
Dirk Keppen, Zentrallblatt MATH -
Readers of New Horizons in Geometry are in for a great ride in the spirit of Archimedes through a beautiful geometrical landscape that will give you considerable pleasure and a heightened appreciation for a wonderful subject.
Don Albers, former Director of MAA Publications
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
-
Chapters
-
Chapter 1. Mamikon’s Sweeping-Tangent Theorem
-
Chapter 2. Cycloids and Trochoids
-
Chapter 3. Cyclogons and Trochogons
-
Chapter 4. Circumgons and Circumsolids
-
Chapter 5. The Method of Punctured Containers
-
Chapter 6. Unwrapping Curves from Cylinders and Cones
-
Chapter 7. New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors
-
Chapter 8. Ellipse to Hyperbola: “With This String I Thee Wed”
-
Chapter 9. Trammels
-
Chapter 10. Isoperimetric and Isoparametric Problems
-
Chapter 11. Arclength and Tanvolutes
-
Chapter 12. Centroids
-
Chapter 13. New Balancing Principles with Applications
-
Chapter 14. Sums of Squares
-
Chapter 15. Appendix
-
In a remarkable display of mathematical versatility and imagination, the authors present us with a wealth of geometrical gems. These beautiful and often surprising results deal with a multitude of geometric forms, their interrelationships, and in many cases, their connection with patterns underlying the laws of nature.
Don Chakerian -
... The authors 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 and extensions of familiar theorems. Lengths, areas and volumes of curves, surfaces and solids are explored from a visually captivating perspective. ... The hundreds of full color illustrations are visually enticing and provide great motivation to read further and savor the wonderful results. This book is a must have for any geometer.
Dirk Keppen, Zentrallblatt MATH -
Readers of New Horizons in Geometry are in for a great ride in the spirit of Archimedes through a beautiful geometrical landscape that will give you considerable pleasure and a heightened appreciation for a wonderful subject.
Don Albers, former Director of MAA Publications
