Title
Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics),New
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In recent years, I have been teaching a juniorseniorlevel course on the classi cal geometries. This book has grown out of that teaching experience. I assume only highschool geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books IIV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various nonEuclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a onesemester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.
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- Q: What topics are covered in 'Geometry: Euclid and Beyond'? A: The book explores classical geometries, starting with a critical examination of Euclid's Elements, and includes modern answers to questions arising from this reading. Key topics include Hilbert's axioms, Cartesian planes, area theory, field extensions, non-Euclidean geometries, and Platonic solids.
- Q: What prior knowledge is required to understand this book? A: A basic understanding of high-school geometry and some abstract algebra is assumed. The book is designed for junior-senior level courses.
- Q: Is this book suitable for self-study? A: Yes, while it is intended for classroom use, the book can also be a valuable resource for self-learners interested in classical geometry and its modern interpretations.
- Q: How many pages does the book have? A: The book contains 540 pages.
- Q: What is the binding type of this book? A: The book is available in hardcover binding.
- Q: Who is the author of 'Geometry: Euclid and Beyond'? A: The author of the book is Robin Hartshorne.
- Q: When was 'Geometry: Euclid and Beyond' published? A: The book was published on June 8, 2000.
- Q: What edition of the book is available? A: This is the corrected edition published in 2000.
- Q: What is the condition of the book? A: The book is in new condition.
- Q: In which category is this book listed? A: The book is categorized under Geometry & Topology.