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College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) [Paperback]

Nathan Altshiller-Court

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Book Description

25 April 2007 0486458059 978-0486458052 2nd
Translated into many languages, this book has been the standard university-level text for decades. Revised and enlarged by the author in 1952, it offers today's students exercises in construction problems, similitude, and homothecy, properties of the triangle and the quadrilateral, harmonic division, and circle and triangle geometry.

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College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) + Advanced Euclidean Geometry (Dover Books on Mathematics) + Geometry: A Comprehensive Course (Dover Books on Mathematics)
Price For All Three: 29.49

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Product details

  • Paperback: 336 pages
  • Publisher: Dover Publications Inc.; 2nd edition (25 April 2007)
  • Language: English
  • ISBN-10: 0486458059
  • ISBN-13: 978-0486458052
  • Product Dimensions: 22 x 14 x 2 cm
  • Amazon Bestsellers Rank: 258,137 in Books (See Top 100 in Books)

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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most Helpful Customer Reviews on (beta) 3.2 out of 5 stars  6 reviews
48 of 49 people found the following review helpful
5.0 out of 5 stars A classic on Euclidean geometry 22 Jun 2007
By J. Bogaarts - Published on
Format:Paperback|Verified Purchase
Thank you Dover!! This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book contains all the classical theorems with full proofs, including many theorems that belong to the so called triangle geometry that was developed in the last quarter of the nineteenth century. Due to geometry software the subject is becoming popular again. The book also contains a treasure of exercises, but no solutions which could be a nuisance. But what use are the solutions? Problems should be solved and not looked up!. Many problems are about geometric constructions. If you prepare for a mathematical contest or if you are interested in a complete overview of the classical plane geometry (for instance after reading Ross Honsberger's "Episodes"), this is your book.

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.
1 of 3 people found the following review helpful
3.0 out of 5 stars Fills a Niche 6 Aug 2013
By CC - Published on
Format:Paperback|Verified Purchase
A rather boring, talkative book on "college geometry;" one would be better off using Johnson's Advanced Euclidean Geometry (also from Dover). Big warning: Very few colleges actually offer geometry courses in Euclidean geometry, which is what this book covers. The biggest feature of this book is its plethora of construction problems. While fun for those who enjoy such problems, it is of little use to anyone at the college level, save perhaps math education majors (and even then, that is doubtful), and of even less use to math contest participants. Few of these types of problems pop up, and a thorough understanding of Euclidean geometry is sufficient to tackle them. Enjoy the book for some unique problems if you have the time and extra pocket change, but it won't change your view on the world or geometry. This would not be my first choice to give, but for the student who has breezed through everything else, this provides a nice change of pace.
This book assumes a STRONG background in high school geometry, particularly in synthetic (i.e. proof based without co-ordinates) geometry.
0 of 2 people found the following review helpful
4.0 out of 5 stars A valuable book for the post 101 geometer 12 Aug 2013
By mr. d. - Published on
Format:Paperback|Verified Purchase
What Altshiller presents here is the cleanup of Roger Johnson's 1929 "Modern Geometry", which summarized the Euclidean geometry up to its time, was user unfriendly, quick-fixing in proofs and dumped most of the work onto the reader rather than giving the appropriate explanations.
Altshiller's book follows the concept of Johnson's. It is reviewed, and most of the mistakes are removed, if there were any. He brings exercises without solutions, type one which result d i r e c t l y out of the previous lesson and are actually fun to be worked out, and type two "supplementary exercises", often far beyond the theorems nearby and excessively difficult. This group should have been presented with hints and solutions - because, the way they stand now, some of them will never be solved.
Also, another modern edition would do some good, including a larger format and computerized (sketchpad) diagrams.
The difficult chapter on i n v e r s i o n with the new tricks You must learn
there runs too short in my opinion.
While the book is "intensively used", the paperback version falls apart.
In summary: a valuable addition on the small market of good geometry publications.
5 of 10 people found the following review helpful
3.0 out of 5 stars They could have made the book bigger 12 Jun 2011
By O. Long - Published on
Format:Paperback|Verified Purchase
The book reads well, but handles badly. This type of book should be printed on larger paper and have a spine that makes it easy to lay it open. If you're drawing the diagrams its hard to keep the book open while you draw. The geometry is excellent, the physical aspects of the book not so much.
3 of 7 people found the following review helpful
3.0 out of 5 stars Great for a College level mathematician. 31 Dec 2012
By lgib - Published on
Format:Paperback|Verified Purchase
This book was chosen for a high school math competition. One of my best competitors and outstanding math students had great difficulty with the material. As the coach, I found the diagram placement and the choice of labeling difficult to follow.
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