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Geometry Revisited (New Mathematical Library) Paperback – 1967

ISBN-13: 978-0883856192 ISBN-10: 0883856190 Edition: 1ST

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Product Details

  • Series: New Mathematical Library (Book 19)
  • Paperback: 193 pages
  • Publisher: The Mathematical Association of America; 1ST edition (1967)
  • Language: English
  • ISBN-10: 0883856190
  • ISBN-13: 978-0883856192
  • Product Dimensions: 6 x 0.7 x 9 inches
  • Shipping Weight: 10.4 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #260,449 in Books (See Top 100 in Books)

Editorial Reviews

Review

'The book is rich in remarkable facts and thereby is very effective in promoting the significance and the value of geometry in mathematical teaching, a promotion which is very necessary.' Mathematical Reviews

Book Description

Among the many beautiful and nontrivial theorems in geometry found here 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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Customer Reviews

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The proofs are very clear and easy to follow.
M. Goldberg
I highly recommend this book to any high school or undergrad teachers and students.
Wing
I can tell you that you will learn multitudes and enjoy the book too.
Reader

Most Helpful Customer Reviews

65 of 66 people found the following review helpful By A Customer on July 25, 2001
Format: Paperback Verified Purchase
This is 'the book' the typical high school student in America needs to read in order to see what Geometry is really all about. Geometry can be fun and engaging. Unfortunately it has taken a back seat in the high school curriculum. This is unfortunate considering the beauty that the subject has to offer. Many topics are covered in this book: The extended law of cosines, Ptolemy's theorem, transformational geometry, conics, and many, many, many more. This is also a book that is essential for mathematical problem solvers-- particularly for those interested in competing. All that is needed to follow along is the basic geometry learned at the high school level. This book is a must have for any mathematical library.
A++ Highly recommended.
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69 of 73 people found the following review helpful By Reader on August 10, 2002
Format: Paperback
I am a high school student who competes in extracurricular mathematics contests. I've found many great books for trigonometry, algebra, precalculus, calculus, and any other field of math except geometry, i.e. until I found this book. A thorough knowledge of geometry beyond what you learn in high school in necessary needed to be competitive, and the place to get it is Geometry Revisited. This book covers any geometry you could need and is by far the best, if not the only, book out there with what you need to know. This book was also very interesting and thought provoking. The selection and arrangement of topics couldn't be any better. Each lesson even contains exercises (with answers and hints) to show you how to apply what the book teaches you. I would recommend this book to any high school student competing in any contests, to any person interested in extending their knowledge of geometry, or to anyone who with any interest in math. I can tell you that you will learn multitudes and enjoy the book too.
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39 of 41 people found the following review helpful By another reader on May 27, 2004
Format: Paperback
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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42 of 45 people found the following review helpful By Wing on July 7, 2000
Format: Paperback
Geometry Revisited should be used as a textbook for every geometry class in high school. It offers comprehensive proofs and theorems that every undergrad should know by the time he/she gets through basic geometry. The last sections of this book also offers a slight touch on comcepts such as non-Eucledian and projective geometry, serving as a launchpad to higher levels of education. I highly recommend this book to any high school or undergrad teachers and students.
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8 of 8 people found the following review helpful By David Jimenez on March 22, 2009
Format: Paperback Verified Purchase
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.
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9 of 10 people found the following review helpful By Charles Saunders on October 29, 2007
Format: Paperback Verified Purchase
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.
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4 of 5 people found the following review helpful By Nona on June 7, 2009
Format: Paperback
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.
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