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Lines and Curves: A Practical Geometry Handbook 2004th Edition

5 out of 5 stars 2 customer reviews
ISBN-13: 978-0817641610
ISBN-10: 0817641610
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Product Details

  • Paperback: 156 pages
  • Publisher: Birkhäuser; 2004 edition (August 27, 2004)
  • Language: English
  • ISBN-10: 0817641610
  • ISBN-13: 978-0817641610
  • Product Dimensions: 6.1 x 0.4 x 9.2 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #972,605 in Books (See Top 100 in Books)

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24 of 25 people found the following review helpful By Mathemagician on March 22, 2006
Format: Paperback Verified Purchase
If you read *one* mathematics book in you whole life, this should be it. No, it will not help you do your taxes or win the lottery. It may, however, change the way you look at the world and give you a serious appreciation of what mathematics as a creative endeavor is about. "Lines and Curves" is an invitation to Euclidean geometry from a dynamic perspective. It will teach you how to think about points in motion rather than visualizing figures as static entities. The exposition is so clear and the examples so well chosen that the barest background will allow you to follow the entire exposition. If you half-remember the concepts of congruence and similarity of triangles you are well on your way to enjoying the intellectual ride of a lifetime (a very concise appendix summarizes the formal prerequisites). Hundred of exquisite exercises are a pleasure to try, varying in difficulty from easy to moderately difficult.

The style is engaging and entertaining. I invite anyone to read the Introduction (available free from Amazon) to get a taste of the material. To keep my comments concrete, consider Chapter 2, "The Alphabet": no fewer than six different interpretations of a straight line as a geometric locus are explained (and will consistently be used throughout the rest of the book). The same goes for the circle, for which at least four interpretations are given. Other conics (ellipses, parabolas, hyperbolas) are treated similarly in Chapter 6.

A further remarkable feature is the authors' willingness to employ analytic geometry at crucial places where resorting to purely synthetic methods would be cumbersome and not particularly illuminating.
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5 of 6 people found the following review helpful By David Gurevich on July 14, 2010
Format: Paperback
Victor Gutenmacher's work Lines and Curves has been a valued part of my library for 6 years. The clever problems inside this work have amused and challenged me, and are excellently instructive.

This work takes you right into the details of solving problems relating to lines and curves. The illustrations that helpfully accompany it are useful and relevant and really add to the learning experience.

Topics it covers include: Sets, points, lines, intersections, curves - and that's just getting started!

If you are looking to learn about geometry, or teach a class on the subject, this book is definitely something you would want to consider. It is a great value.
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