Revolutions of Geometry
Language: English
Published by John Wiley and Sons Ltd, 2010
- First Edition
- Hardcover
- New
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, IrelandKennys Bookshop and Art Galleries Ltd.
AbeBooks seller since February 27, 2001
Condition: New
£ 158.97
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2010. 1st Edition. Hardcover. Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Num Pages: 608 pages, Illustrations. BIC Classification: PBM; PDX. Category: (UU) Undergraduate. Dimension: 236 x 164 x 35. Weight in Grams: 988. . . . . .
Seller Inventory # V9780470167557
- Title
- Revolutions of Geometry
- Author
- Michael L. O?Leary
- Publisher
- John Wiley and Sons Ltd
- Publication year
- 2010
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0470167556
- ISBN 13
- 9780470167557
- Edition
- 1st Edition
In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems.
Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries.
The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics.
Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.
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Kennys Bookshop and Art Galleries Ltd.
Galway, GY, Ireland
AbeBooks seller since February 27, 2001
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