{"product_id":"revolutions-of-geometry-isbn-9780470167557","title":"Revolutions of Geometry","description":"\u003cb\u003eGuides readers through the development of geometry and basic proof writing using a historical approach to the topic\u003c\/b\u003e  \u003cp\u003eIn an effort to fully appreciate the logic and structure of geometric proofs, \u003ci\u003eRevolutions of Geometry\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eFollowing 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 \u003ci\u003eElements.\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eWell organized and clearly written, \u003ci\u003eRevolutions of Geometry\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgements xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Foundations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1 The First Geometers 3\u003c\/p\u003e \u003cp\u003e2 Thales 27\u003c\/p\u003e \u003cp\u003e3 Plato and Aristotle 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II The Golden Age\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4 Pythagoras 87\u003c\/p\u003e \u003cp\u003e5 Euclid 123\u003c\/p\u003e \u003cp\u003e6 Archimedes 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Enlightenment\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7 François Viète 227\u003c\/p\u003e \u003cp\u003e8 René Descartes 267\u003c\/p\u003e \u003cp\u003e9 Gérard Desargues 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV A Strange New World\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10 Giovanni Saccheri 323\u003c\/p\u003e \u003cp\u003e11 Johann Lambert 353\u003c\/p\u003e \u003cp\u003e12 Nicolai Lobachevski and János Bolyai 393\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V New Directions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13 Bernhard Riemann 443\u003c\/p\u003e \u003cp\u003e14 Jean-Victor Poncelet 483\u003c\/p\u003e \u003cp\u003e15 Felix Klein 519\u003c\/p\u003e \u003cp\u003eReferences 565\u003c\/p\u003e \u003cp\u003eIndex 573\u003c\/p\u003e \"An excellent supplemental resource or main textbook for an overview of mathematics course for upper-level undergraduate and graduate students.\" (Choice, October 2010). \u003cb\u003eMichael O'Leary\u003c\/b\u003e, PhD, is Professor of Mathematics at the College of DuPage. He received his PhD in mathematics from the University of California, Irvine in 1994.  \u003cb\u003eGuides readers through the development of geometry and basic proof writing using a historical approach to the topic\u003c\/b\u003e  \u003cp\u003eIn an effort to fully appreciate the logic and structure of geometric proofs, \u003ci\u003eRevolutions of Geometry\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eFollowing 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 \u003ci\u003eElements.\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eWell organized and clearly written, \u003ci\u003eRevolutions of Geometry\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989961588965,"sku":"NP9780470167557","price":166.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470167557.jpg?v=1761786041","url":"https:\/\/k12savings.com\/es\/products\/revolutions-of-geometry-isbn-9780470167557","provider":"K12savings","version":"1.0","type":"link"}