Advanced Euclidean Geometry (Dover Books on Mathematics)

by Roger A. Johnson (Author)

5 customer reviews

ISBN-13: 978-0486462370

ISBN-10: 0486462374

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For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises.
The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

Advanced Euclidean Geometry (Dover Books on Mathematics)

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Product Details

Series: Dover Books on Mathematics
Paperback: 319 pages
Publisher: Dover Publications (August 31, 2007)
Language: English
ISBN-10: 0486462374
ISBN-13: 978-0486462370
Product Dimensions: 8.5 x 5.4 x 0.6 inches
Shipping Weight: 11.2 ounces (View shipping rates and policies)
Average Customer Review: 4.6 out of 5 stars See all reviews (5 customer reviews)
Amazon Best Sellers Rank: #668,847 in Books (See Top 100 in Books)
- #77 in Books > Science & Math > Mathematics > Geometry & Topology > Algebraic Geometry
- #288 in Books > Textbooks > Science & Mathematics > Mathematics > Geometry

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Customer Reviews

4.6 out of 5 stars

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70 of 71 people found the following review helpful

A Classic on Euclidean geometry

By J. Bogaarts on September 16, 2007

Format: Paperback

Recently Dover has reissued two classics on Euclidean geometry, College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) and this book. Both books were originally issued in the first half of the 20th century and both were aimed at a college level audience. Both of them also have a considerable amount of so called triangle geometry. As triangle geometry has seen a large upsurge the last years, especially during the last two decennia, there is certainly a need for an English book that gives an overview of the subject including the recent results. These books are useful in this respect but as they are both from the first half of the 20th century, they are out of date. Until a modern treatment of the subject will be available, these two books and the resources on the www will have to do. Altshiller Courts' book has a great set of exercises that can be used as a training ground for geometric problem solving. The problems in Johnsons' book mostly ask for proofs of theorems that are ommited in the text (that's why I give 4 stars). Another drawback of Johnsons' book is that there is no attention paid to geometric constructions. If you are interested in the subject, buy both, its certainly value for money.

The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry.Read more ›

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9 of 10 people found the following review helpful

Great, but Not Wonderful

By Cory Dean on August 5, 2013

Format: Paperback Verified Purchase

If you enjoyed proofs in high school geometry, this will be a pleasure to work through. Without being bogged down by calculations or coordinates, this book presents some of the more famous (to contest participants) and advanced theorems of Euclidean geometry. This should be required for anyone working towards olympiad level geometry and any math team coaches. Be warned that, though still a minority in terms of the type of problems, this book has no constructions. For that, I recommend (albeit reluctantly due to a lack of better alternatives) Altshiller-Court's College Geometry.
Previous reviewers are correct to say that most of the problems are just proofs of stated theorems, but that is what most higher math textbooks do. You'll be surprised to find, though, that even just those proofs are sufficient to cement the knowledge found in this cheap and small book in your head. For a variety of applications and more interesting exercises, a next step with this material (though more of a lateral move in terms of content and downwards move in terms of difficulty) is Coexeter's Geometry Revisited.
This book assumes a STRONG background in high school geometry.

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1 of 4 people found the following review helpful

Five Stars

By Amazon Customer on August 22, 2014

Format: Kindle Edition Verified Purchase

Great Price!!!

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0 of 3 people found the following review helpful

Geometry Rules!

By PhilN on October 7, 2014

Format: Paperback

Nice, classic treatment. Everything you wished you had learned after your first course in geometry.

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0 of 4 people found the following review helpful

RELIABLE

By ADAMIAK BOOKS-ABAA on September 24, 2014

Format: Paperback Verified Purchase

accurate and speedy

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