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Geometry Revisited (Mathematical Association of America Textbooks)
Binding: Paperback
Author: H. S. M. Coxeter
Manufacturer: The Mathematical Association of America
Availability: Usually ships in 24 hours
Average Rating: 5.0
Total Customer Reviews: 8
List Price: $29.95
Our Price: $26.95
Sales Rank: 91043
Product Description
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
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Users Product Reviews: |
Product Review Summary: Fun and hard If you pass through the Geometry, the book is fun and light. If you study the Geometry again, the book is honest and hard.
Product Review Summary: An excellent book on elementary Euclidean geometry This book, which has been available for quite some time, is still a great place to learn about topics in Euclidean geometry which you probably will not cover in a typical middle or high school math class. The level is completely elementary, meaning that anyone with knowledge of pre-calculus will be able to read this book (if they are sufficiently dedicated). The quality of the exposition is superb, and the mathematical content is interesting and varied.
While people who are interested in recreational mathematics will definitely find this book interesting, perhaps the audience for which this book will be most profitable are middle and high school students preparing for mathematics competitions. It is a considerable advantage, especially for the more difficult competitions, to know the techniques and theorems covered in this book.
If you're interested in learning geometry you may not have covered in school, or are preparing for math competitions, buy this book.
Product Review Summary: The best text on Elementary Geometry in English This is one of my three favorite texts in Elementary Geometry, and the only one written in English. It's a multipurpose text. You will probably won't cover these material at school, but if you are interested on math contests, or more serious geometry study, this is also a good text to follow to learn, or if you, like me, learned most of this material over a decade ago, but need a good text as a reference, this text is a great to do so. Dearly recommended.
Product Review Summary: Great book This is a wonderful book if you want to gain a real understanding of what geometry can be (if you like this book you should buy the biography of Coxeter: "King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry" - it is one of the best biographies of a mathematician on the market and shows that Coxeter was a genius and a hoot). However, if you know a significant amount of geometry, then try "Introduction to Geometry, 2nd Edition" as that is the more complete (and (very) much more rigorous) text. Also, if you like this book, then buy "Visual Complex Analysis".
PS. My son is using this book in his high school geometry course (at my insistence) rather than the 'text' he was issued. He is now assisting the teacher with the proofs and problems.
Product Review Summary: Incredibly helpful I just worked through this book & I have to say that it's probably the best for "what's next" after high school geometry. It's got a chapter on each of the following things: triangles (with Ceva's & Steiner-Lehmus' theorems, orthic triangles & Euler lines, etc), circles (like power of a point, etc), collinearity & concurrence, transformations (Yaglom's series of 3 books are better for these though but this is a good introduction), and an intro to inversive geometry and projective geometry. One section that blew my mind is the one about the "3-jugs" problem where you've got a jug that holds 8L, one that holds 5L & one the holds 3L and the goal is to get 4L in each of two jugs. Maybe you've heard of it...? This book gives a general method for solving problems like that using reflections. I liked how each section is very short and typically has just 2-3 theorems, so the book is split into manageable pieces. Maybe it's just a psychological thing, but I like that. Depending on the section, there are 3-10 problems at the end of each section; like any book there are easy ones with fairly obvious solutions and there are hard ounes that take a lot of thought. I think the hard ones might have come from olympiads because Sam Greitzer was a USAMO coach at some point. It doesn't matter though, this book gives you a lot of tools you can use to deal with olympiad-level problems. A couple good ones to work on after this book would be Johnson's "Advanced Euclidean Geometry" and Court's "College Geometry", both out of print unfortunately but maybe a nearby library wold have them?
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