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Resolutions Eligible for refund or replacement
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Clarence Raymond Wylie
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Introduction to Projective Geometry (Dover Books on Mathematics) Illustrated Edition

by C. R. Wylie Jr. (Author), Mathematics (Author)
4.2 4.2 out of 5 stars 29 ratings
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This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
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  1. ISBN-10
    048646895X
  2. ISBN-13
    978-0486468952
  3. Edition
    Illustrated
  4. Publisher
    Dover Publications
  5. Publication date
    December 9, 2008
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    6.1 x 1.2 x 9.1 inches
  9. Print length
    574 pages
  10. See all details
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Editorial Reviews

About the Author

C. R. Wylie was an instructor at the University of Utah.

A Dover Original
Clarence Raymond Wylie, Jr., had a long career as a writer of mathematics and engineering textbooks. His Advanced Engineering Mathematics was the standard text in that field starting in the 1950s and for many decades thereafter. He also wrote widely used textbooks on geometry directed at students preparing to become secondary school teachers, which also serve as very useful reviews for college undergraduates even today. Dover reprinted two of these books in recent years, Introduction to Projective Geometry in 2008 and Foundations of Geometry in 2009.

The author is important to our program for another reason, as well. In 1957, when Dover was publishing very few original books of any kind, we published Wylie's original manuscript 101 Puzzles in Thought and Logic. The book is still going strong after 55 years, and the gap between its first appearance in 1957 and Introduction to Projective Geometry in 2008 may be the longest period of time between the publication of two books by the same author in the history of the Dover mathematics program. Wylie's 1957 book launched the Dover category of intriguing logic puzzles, which has seen the appearance of many books by some of the most popular authors in the field including Martin Gardner and, more recently, Raymond Smullyan.

Here's a quick one from 101 Puzzles in Thought and Logic:

If it takes twice as long for a passenger train to pass a freight train after it first overtakes it as it takes the two trains to pass when going in opposite directions, how many times faster than the freight train is the passenger train?

Answer: The passenger train is three times as fast as the freight train.

Product details

  • Publisher ‏ : ‎ Dover Publications; Illustrated edition (December 9, 2008)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 574 pages
  • ISBN-10 ‏ : ‎ 048646895X
  • ISBN-13 ‏ : ‎ 978-0486468952
  • Item Weight ‏ : ‎ 1.6 pounds
  • Dimensions ‏ : ‎ 6.1 x 1.2 x 9.1 inches
  • Customer Reviews:
    4.2 4.2 out of 5 stars 29 ratings

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Clarence Raymond Wylie

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Customer reviews

4.2 out of 5 stars
4.2 out of 5
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29 global ratings

Top reviews from the United States

An_Amazon_Customer
5.0 out of 5 stars Does it all (2-dimensions), axiomatic AND analytic!
Reviewed in the United States on June 16, 2017
Verified Purchase
I thought I'd written a review when I finished the book, but recently discovered I hadn't. Major oversight!

This is a wonderful book. Wylie has "written it all down", approaching the subject of the projective plane from both an analytic viewpoint (using linear algebra), AND an axiomatic one. No other author I've read had the patience to do so. He even takes the axiomatic approach far enough to introduce coordinates, for Pete's sake! Of course he treats conics at length, a subject I always find amazing. (How can such a beautiful theory of "curvey" curves arise from a bare-bones theory of STRAIGHT lines?)

One can view the dual treatment of the projective plane (axiomatic AND analytic) this way: Wylie sets up and explores an axiomatic system, and then shows very carefully that a model for the system is the usual coordinate-based one we get from linear algebra. We're not entitled to apply the results of the axiomatic treatment, in a coordinate setting, until we've established this crucial connection.

(This is not Wylie's point of view, however. I think his intention is more pedagogical. First, give a "concrete" example of the projective plane by building on the reader's knowledge of linear algebra, and after getting some experience with that, start over to develop the theory from a small set of axioms.)

A signifcant omission from Wylie's axiomatic treatment is the subject of 2-dimensional projectivities (automorphisms of the projective plane).

Having done my best to praise the book, I wouldn't necessarily recommend it for someone with NO prior exposure to projective geometry. Maybe I'm just too stupid, but I think it would be confusing to someone who didn't already have some feeling for the major outlines of the subject. For the novice looking for an introduction, I would recommend Coxeter's "Projective Geometry". It's mainly synthetic, and presumes no knowledge of linear algebra.
11 people found this helpful
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Richard Wood
5.0 out of 5 stars Good vendor
Reviewed in the United States on July 14, 2021
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Product quality matched description; delivery time as stated.
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Twelve Speeds Are Enough
4.0 out of 5 stars with a really nice (and challenging
Reviewed in the United States on April 19, 2018
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VERY thorough and CONCRETE introduction, with a really nice (and challenging!) chapter at the beginning looking at projection from the original historical and very visual point of view. So a great place to start your journey to the heights of projective geometry and its uses in algebraic geometry.
4 people found this helpful
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ANDRE C. DASILVA
5.0 out of 5 stars From the fundamentals to the metric gauges in projective geometry
Reviewed in the United States on November 1, 2019
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A wide, clear, and outstanding pedagogical presentation of projective geometry, this book is a great value for students, engineers and mathematicians.
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Jose Luis Leganes Nieto
4.0 out of 5 stars ... and it is a goog approach to get a perfect image on projective geometry
Reviewed in the United States on February 4, 2017
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It was a new subject for me and it is a goog approach to get a perfect image on projective geometry.
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Arzi
5.0 out of 5 stars exactement ce que je cherchais
Reviewed in France on August 21, 2019
Verified Purchase
Ce livre correspond exactement à ce que je voulais. Parfait.
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Peter Michael Grant
1.0 out of 5 stars THIS BOOK WAS PRINTED WITH A DISGUSTING PERFUME, LIKE FEBREZE - TOTALLY UNACCEPTABLE - AMOUNTING ...
Reviewed in the United Kingdom on February 9, 2018
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THIS BOOK WAS PRINTED WITH A DISGUSTING PERFUME, LIKE FEBREZE - TOTALLY UNACCEPTABLE - AMOUNTING TO THEFT
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Jiang Menghua
5.0 out of 5 stars Received in good condition, way ahead of schedule
Reviewed in Singapore on November 2, 2022
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The book is received in good condition and nearly a week ahead of the indicated delivery date.
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anonymer Anwender
5.0 out of 5 stars Wylie hat das ein Buch verfasst, Hut ab.
Reviewed in Germany on December 8, 2014
Verified Purchase
Es ist gewissermaßen episch breit und tief. Aber insgesamt lesbar, nachvollziehbar und hat auch einige sehr griffige Formulierungen für Theoreme und Corrolare. Für einen Geometrie Fan, eine leichte Entscheidung.
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RM
5.0 out of 5 stars Un manuale intramontabile
Reviewed in Italy on May 18, 2014
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Concisione, chiarezza, semplicità del ragionamento. La discussione analitica prevale su quella sintetica, cioè grafica, e questo è l'unica scelta dell'Autore che mi sento di mettere in discussione. Per il resto si tratta di un testo utilissimo, non solo divulgativo, che colloca la geometria proiettiva nel contesto storico senza rinunciare ad una trattazione attuale.
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