Geometry Revisited (New Mathematical Library)

Rating:
Summary: FOR ALL THOSE INTERESTED IN MATHEMATICS
Review: 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.

Rating:
Summary: THE BEST SOURCE FOR GEOMETRY
Review: 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.

Rating:
Summary: Incredibly helpful
Review: 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?

Rating:
Summary: FOR ALL THOSE INTERESTED IN MATHEMATICS
Review: 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.