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College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) 2nd Revised ed. Edition

4.3 4.3 out of 5 stars 37 ratings
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Translated into many languages, this book was in continuous use as the standard university-level text for a quarter-century, until it was revised and enlarged by the author in 1952. World-renowned writer and researcher Nathan Altshiller-Court (1881–1968) was a professor of mathematics at the University of Oklahoma for more than thirty years. His revised introduction to modern geometry offers today's students the benefits of his many years of teaching experience.
The first part of the text stresses construction problems, proceeding to surveys of similitude and homothecy, properties of the triangle and the quadrilateral, and harmonic division. Subsequent chapters explore the geometry of the circle — including inverse points, orthogonals, coaxals, and the problem of Apollonius and triangle geometry, focusing on Lemoine and Brocard geometry, isogonal lines, Tucker circles, and the orthopole. Numerous exercises of varying degrees of difficulty appear throughout the text.
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  1. ISBN-10
    0486458059
  2. ISBN-13
    978-0486458052
  3. Edition
    2nd Revised ed.
  4. Publisher
    Dover Publications
  5. Publication date
    April 19, 2007
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    5.39 x 0.65 x 8.48 inches
  9. Print length
    336 pages
  10. See all details
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Editorial Reviews

About the Author

Nathan A. Court taught geometry at the University of Oklahoma for more than 30 years and is the author of Mathematics in Fun and Earnest.

Product details

  • Publisher ‏ : ‎ Dover Publications; 2nd Revised ed. edition (April 19, 2007)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 336 pages
  • ISBN-10 ‏ : ‎ 0486458059
  • ISBN-13 ‏ : ‎ 978-0486458052
  • Item Weight ‏ : ‎ 12.5 ounces
  • Dimensions ‏ : ‎ 5.39 x 0.65 x 8.48 inches
  • Customer Reviews:
    4.3 4.3 out of 5 stars 37 ratings

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Nathan Altshiller-Court

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4.3 out of 5 stars
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37 global ratings

Top reviews from the United States

J. Bogaarts
5.0 out of 5 stars A classic on Euclidean geometry
Reviewed in the United States on June 22, 2007
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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 .
57 people found this helpful
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mr. d.
4.0 out of 5 stars A valuable book for the post 101 geometer
Reviewed in the United States on August 12, 2013
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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.
3 people found this helpful
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RogerOverAndOut
1.0 out of 5 stars A bad precident for the subject.
Reviewed in the United States on January 9, 2013
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I purchased this book in order to learn about different shapes and their parameters and names as I've always had an interest in geometry and shapes, and thus far have only taken a few college level trig/algebra classes, and to my knowledge my local community college doesn't even have a geometry class. I found this book difficult to follow and the author's use of english language foreign to the common United States English language speaker. He starts out with the words to instuctor explaining how geometry has lost popularity over the years, and in the words to the student he hits home the proof as to why that is the trend. lol. I'm definately going to look elsewhere to learn about geometry. Also I agree with the comment about the book being too small.
3 people found this helpful
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O. Long
3.0 out of 5 stars They could have made the book bigger
Reviewed in the United States on June 12, 2011
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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.
10 people found this helpful
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lgib
3.0 out of 5 stars Great for a College level mathematician.
Reviewed in the United States on December 31, 2012
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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.
3 people found this helpful
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