Barron’s Painless Geometry, by Lynette Long
I have to admit that this book disappointed me a little bit. It is not that the book is bad. It is indeed a modestly enjoyable book that I would have liked a lot more had I read it during late elementary or middle school when I was engaged in that stage of my personal math development. It is a book I could also recommend to those in the same age range who want some assistance in better understanding geometry from a conventional standpoint of formal learning in plane geometry. I was disappointed not by its contents but by the fact that I was expecting at least some treatment of spherical geometry and its quirks, and this book did not manage that task at all. I am not sure that any study of geometry could be viewed by those who are terrified of the subject matter as painless, but if you want a suitably silly look at plane geometry that will give some help in understanding what a high school level understanding of the subject matter would require, this book certainly does fine. But sometimes one simply wants more and that is too advanced of a subject for this book to cover, I suppose.
This book is between 350 and 400 pages long, although it reads fast because the pages are small and there are a lot of pictures, and it contains eleven chapters. The book begins with a short introduction and after that discusses some terms (1). After that the author discusses angels (2) and then parallel and perpendicular lines (3). There is a chapter on triangles (4) and then a chapter on congruent and similar triangles (5). This leads to a discussion of quadrilaterals (6) and polygons (7), as well as circles (8). Unsurprisingly, having discussed these two-dimensional shapes the author then covers perimeter, area, and volume (9), after which there is a lot of helpful discussion of graphing using various methods (10). The last chapter discusses constructs (11), after which there are appendices that include a glossary (i) as well as key formulas (ii), followed by an index. As a whole, the chapters themselves include quite a few exercises for the reader to work out and plenty of problems as well to sort out the understanding the reader has of the subject, with the answers included at the end of each chapter so as to help the reader to understand one subject before moving on to the next one.
It is worthwhile to celebrate some of the ways this book seeks to be painless and how it seeks to further the understanding of a subject that is somewhat dry and formal for many students. The book encourages experiments as a practical means of understanding geometry so that one can actually understand the relevance of the area of study instead of simply memorizing equations without understanding, as is frequently the case in many classes of the subject. Similarly, the book uses a lot of illustrations so as to help the reader understand the book’s subject material. All of this makes the book certainly a lot more fun than the usual geometry book, and a far more entertaining entree into the subject subject than most geometry textbooks would be. It is up to the reader, of course, to determine whether one wants an enjoyable if somewhat basic book on the subject or one is looking for more advanced offerings. Still, if you want a book for a young geometry student who needs to visualize something in order to better understand the material, this book is certainly a worthwhile one that I can recommend from my own reading of it.