Introduction to Projective Geometry

Format: Paperback
Pub. Date: 2008-12-09
Publisher(s): Dover Publications
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This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.

Author Biography

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.

Table of Contents

The Elements of Perspective
The Extended Euclidean Plane
A Little Linear Algebra
Further Properties of the Extended Plane
Linear Transformation in II(subscript)2
The Axiomatic Foundation
The Complete Four-point and Complete Four-line
The Introduction of Coordinates
The Introduction of a Metric
Singular Metric Gauges
A Review of Determinants
A Finite Nondesarguesian Geometry
Answers to Odd-numbered Exercises

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