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New horizons in geometry / Tom M. Apostol and Mamikon A. Mnatsakanian.
- Format:
- Book
- Author/Creator:
- Apostol, Tom M., author.
- Mnatsakanian, Mamikon A., author.
- Mnatsakanian, Mamikon A., author, illustrator.
- Series:
- Dolciani mathematical expositions ; no. 47.
- Dolciani mathematical expositions ; no. 47
- Language:
- English
- Subjects (All):
- Geometry.
- Calculus.
- Physical Description:
- 1 online resource (xiv, 513 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Washington : Mathematical Association of America, 2012.
- Summary:
- 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.
- Contents:
- Mamikon's sweeping-tangent theorem
- Cycloids and trochoids
- Cyclogons and trochogons
- Circumgons and circumsolids
- The method of punctured containers
- Unwrapping curves from cylinders and cones
- New descriptions of conics via twisted cylinders, focal disks, and directors
- Ellipse to hyperbola : "with this string I thee wed"
- Trammels
- Isoperimetric and isoparametric problems
- Arclength and tanvolutes
- Centroids
- New balancing principles with applications
- Sums of squares.
- Notes:
- Includes bibliographical references and index.
- Title from publisher's bibliographic system (viewed on 02 Oct 2015).
- ISBN:
- 1-61444-210-X
- OCLC:
- 852801469
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