This book is a genuine math book, not a mere popularization of mathematical ideas. Despite the fact that it has only 174 pages, of which 80 are dedicated to illustrative plates, full appreciation requires a slow “read” of formulas, equations, and tables — especially in the first half of the book, which treats the mathematical features of key proportions and the features of regular plane and solid figures. I was especially fascinated by the extensive discussion of Archimedean solids, which were new to me. The later chapters address the prevalence of such mathematical patterns in biological and artistic phenomena.
With respect to the “geometry of life” (which is treated before art in the book, contrary to the sequence in the title), this book shows its mid-20th-century age by being ignorant of fractal dimension and non-linear self-similarity. The mathematics of natural forms was revolutionized just one generation later than this book’s issuance. The later discoveries of Benoit Mandelbrot and others were greatly facilitated by automated computing. Still, Ghyka’s chapter on the topic is a concise summation of the earlier state of knowledge, and these concepts were not invalidated by fractal geometry.
The most significant portion of the “geometry of art” addresses the use of proportional canons in classical and gothic architecture, as rediscovered by modern scholars. Ghyka endorses a theory of the “transmission of geometrical symbols and plans” which implicates the ancient mysteries and asserts a continuity through medieval stonemasons to modern secret societies. There is no mention, however, of the further participation of isopsephy in the classical schemes. (For that, see David Fideler’s Jesus Christ, Sun of God.) The final chapter discusses conscious and unconscious applications of “symphonic symmetry” in modern art.
I enjoyed this little volume hugely, and I recommend it to anyone who shares my interests in mathematics, morphogenesis, and mysticism. [via]