The Glorious Golden Ratio, by Alfred S. Posamentier and Ingmar Lehmann
Quite honestly, this book disturbed me at least a little bit. There are at least two ways that one can take this book as a reader. One is to see it as a deeply mathematical discussion of how a wide variety of arithmetic and geometrical phenomena involve the golden ratio or any other number of golden elements related to phi (Φ) can be found in math, in architecture, in nature, and even in flags. The other way to look at this book is to see the authors as encouraging a numberism that encourages occult thinking and practice . It is quite possible that some readers of this book will be put off by both the authors’ profound interest in mathematics and frequent use of equations to give somewhat contrived relationships that show the ubiquity of phi in certain areas of mathematics and also disturbed at how this number relates to pentegons, platonic solids, pentegrams, the star of David, the ying-yang symbol, and various aspects of history and architecture. Few books manage to hit its precise target of people interested in both esoteric matters as well as at least moderately advanced mathematics, which is an achievement, I suppose.
This book is more than 300 pages long if one includes its appendices that show proofs and justifications of selected relationships relating to phi not included in the main text, and it should be noted that the endnotes of this book are worth reading because they add some flavor and even some other mildly disturbing reflections on some of the matters discussed in the book. After some acknowledgements and an introduction that talks up the importance of phi, the authors begin the book with a definition and quite a few constructions of the golden ratio (1), which is a hint of things to come. After that the authors discuss the golden ratio as it appears in history (2) and the numerical value of phi and some of its more striking and interesting properties (3). The author then discusses golden geometric figures (basically the platonic solids and a few other ones ) (4) as well as some unexpected appearances of the golden ratio (5). After this the authors give some discussion to the golden ratio as it appears in the plant kingdom (6) as well as the relationship between the golden ratio and fractals (7). Throughout the authors have a vigorous interest in mathematics that ensures that the reader will be wading through many pages of equations and proofs.
Ultimately, my thoughts are somewhat split about this book. On the one hand, I greatly appreciate the intriguing role of phi in history as well as in mathematics, and even if some of the equations can be a challenge to slog through, I think it is ultimately worthwhile to do so at least to better understand why it is that the authors think that January 6th should be Phi Day just as March 14th is Pi day. Even so, there is a great deal about this book that is somewhat troubling. The authors make many contrived relationships to phi and somewhat oversell the presence or possible presence of phi in ancient architecture like the Parthenon and Great Pyramid, which hurts the case of the authors a bit when one examines the importance of phi. Likewise, the interest the authors have in the relationship between phi and matters of religious and occult symbolism including freemasonry, Eastern religious, and kabbalah is more than a bit troubling. Reading a book about mathematics shouldn’t feel as if one is being taught about the Illuminati from a glowing and enthusiastic supporter of such thinking, but this book does feel that way, demonstration of the permeability of fields that one would not normally put together.
 See, for example: