Configurations of Points and Lines (Graduate Studies in Mathematics) by Branko Grunbaum (PDF)

Description

This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author’s contributions are central to this revival. In particular, he initiated the study of 4-configurations (that is, those that contain four points on each line, and four lines through each point); the results are fully described in the text. The main novelty in the approach to all geometric configurations is the concentration on their symmetries, which make it possible to deal with configurations of rather large sizes. The book brings the readers to the limits of present knowledge in a leisurely way, enabling them to enjoy the material as well as entice them to try their hand at expanding it.

User’s Reviews

Editorial Reviews: Review “…the book is almost entirely self-contained, and the author has a tone that is extremely readable… I think many authors could learn a thing or two about readability from Grünbaum, and reading his book was a real pleasure.” —- MAA Reviews”This is the only book on the topic of geometric configurations of points and lines. [It] brings the readers to the limits of present knowledge in a leisurely way, enabling them to enjoy the material as well as enticing them to try their hand at expanding it.” —- Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There is only one Grunbaum! Original research of others and of his own and his students.

⭐Fascinating. Will require much study

⭐The only book on this subject. It is true that this book will bring you to the frontier of current work on configurations without too much pain. The author gets credit for clear, competent writing and good organization. It is also true that the frontier in configurations is not extremely difficult to reach (one semester at the advanced undergrad/ beginning graduate level is more than sufficient to work on open problems). Depending on your viewpoint, this is a hot new field with interesting and accessible open problems, or alternately a field which was invented in the late nineteenth century and then justly neglected for one hundred years until Grunbaum brought it back.While the book is inviting and readable, the editing was not so great. There are a lot of typos or just plain errors, so be prepared to read as a skeptic. I list an example of each below.I have a major complaint about the lack of any use of linear algebra for the combinatorial material. Section 1.7 ignores a lot of well-known graph theory; it’s possible for a student to read this and not realize that the graph isomorphism problem is famous and old. Working by hand with deficiency graphs, etc, to rule out isomorphisms is tedious and completely pointless in the 21st century if your computer can tell you that the eigenvalues of the adjacency matrices differ.Examples to show the lack of editing:–p.49. Most of the second paragraph is devoted to showing that “the automorphism group consists of two elements, the identity and s.” This is false; the group has order four.– p.205. The caption of figure 3.6.2. identifies a configuration as “sporadic.” However it does not appear in the “complete list” of sporadic configurations on p.207, and moreover it is clearly systematic of family (i) with k=2, j=1 in the notation of p.204.

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