Projective Geometry

I was first introduced to Projective Geometry by Lawrence Edwards in an upper level undergraduate Projective Geometry course, and I believe that this book is not like any other math text book that I ever had in my undergraduate career. This may sound strange, but I felt as if this book read more like a novel. Its chapters often include some very philosophical (almost poetic) statements, and new concepts are introduced via constructions. I believe you could call this a synthetic approach to the subject. This made learning and re-leaning projective geometry easier. After I finished the course I would occasionally pick the book up the book, grab a pencil and paper, or (better yet) use The Geometer's Sketchpad and continue on with the book. Yet later on, I preferred having a more direct and concise book (such as the one by H.S.M. Coxeter) text to refer back to. Edwards states in his Foreword that much of the material beyond chapter 13 doesn't appear in this same form anywhere else in English. One of the subjects discussed in chapter 13 and beyond is Von Staudt's theory of the imaginary. I actually did a research project on this topic, and I must agree with Edwards. Many of the projective geometry books that I have read only go far enough to briefly mention that elliptic involutions determine imaginary points. However there are a couple books out there that devote their last chapter to each author's own development of the imaginary. Otherwise, the information comes from scattered articles or foreign language (mostly German) texts. There is one book that I found, J.L.S. Hatton's The Theory of The Imaginary in Geometry: Together with the Trigonometry of the Imaginary that is wholly devoted to the theory of the imaginary. However, Hatton's work is (in my opinion) very dense, and it also includes analytical approaches as well.Furthermore, if you briefly look over the table of contents you will probably find other topics that are not typically presented in other projective geometry books (such as path curves), but the only topics I really searched for dealt with the imaginary.I truly learned a great deal from this book, having read it both for school work and for fun. However, like I mentioned above, I found it sometimes useful to have another book on the subject to refer to at times. Also some of the terms that Edwards uses (e.g. "breathing involution") may actually be his own creation (I'm not sure), and this made cross-referencing the book with other projective geometry texts a little harder. Lastly, I should mention that when I had this book in class my teacher pointed out errors in it, but there were only one or two of them.The Theory Of The Imaginary In Geometry: Together With The Trigonometry Of The Imaginary (1920)Projective GeometryThe Geometer's Sketchpad: Dynamic Geometry Software for Exploring Mathematics

excellent

The author has an unusual approach to the subject. This is not a book for the beginner. There are typographical diagram errors which cause problems.