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College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics), by Nathan Altshiller
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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.
- Sales Rank: #1015706 in eBooks
- Published on: 2012-06-29
- Released on: 2012-06-29
- Format: Kindle eBook
Most helpful customer reviews
51 of 52 people found the following review helpful.
A classic on Euclidean geometry
By J. Bogaarts
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.
8 of 13 people found the following review helpful.
They could have made the book bigger
By O. Long
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.
1 of 3 people found the following review helpful.
Fills a Niche
By Cory Dean
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.
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