Elementary Euclidean Geometry: An Undergraduate Introduction

By C.G. Gibson

This book, first published in 2004, is a genuine introduction to the geometry of lines and conics in the Euclidean plane. Lines and circles provide the starting point, with the classical invariants of general conics introduced at an early stage, yielding a broad subdivision into types, a prelude to the congruence classification. A recurring theme is the way in which lines intersect conics. From single lines one proceeds to parallel pencils, leading to midpoint loci, axes and asymptotic directions. Likewise, intersections with general pencils of lines lead to the central concepts of tangent, normal, pole and polar. The treatment is example based and self contained, assuming only a basic grounding in linear algebra. With numerous illustrations and several hundred worked examples and exercises, this book is ideal for use with undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences.

• Format: Hardcover
• Language: English
• ISBN: 0521834481
• ISBN13: 9780521834483
• Release Date: April 2004
• Publisher: Cambridge University Press
• Length: 192 Pages
• Weight: 1.05 lbs.
• Dimensions: 0.6" x 5.9" x 8.9"

Customer Reviews

Geometry of lines and planes in the Euclidean plane

The content of this book is not what I expected from the title. My thoughts were that it would be a book of traditional geometry, based on the Euclidean set of axioms. Instead, the book covers the geometry of lines and conics in the Euclidean plane. It begins with the representation of points and lines as vectors and how length and distance are computed in the Euclidean plane. From this, the equations of the three standard categories of conics, as well as all of the associated figures such as the asymptotes are examined. Understanding the material requires knowledge of the basics of linear algebra, in particular how to work with matrices and determinants. The presentation is well done, based on a large number of worked examples and many figures. If your interest is in learning the formulaic representations of conics in 2-space, then this book is right for you. However, I do consider the title misleading, the book is not about geometry as we usually consider it in the Euclidean sense. It deals with an application of geometry as applied to a specific class of figures and equations. Published in Journal of Recreational Mathematics, reprinted with permission.