Tag Archives: geometry

The Geometry of Art and Life

Hermetic Library fellow T Polyphilus reviews The Geometry of Art and Life by Matila Ghyka:

Matila Ghyka's The Geometry of Art and Life


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]



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Part III: The Circumference and the Hieroglyphic Monad in In Operibus Sigillo Dei Aemeth by David Richard Jones.

“Curiously, and we have to wonder if it was known or unknown to Dee, the geometry of the Monad as analyzed and expected in Theorem XXIII when applied to a circle subdivides the circumference of a circle into seven equal divisions with almost perfect elegance. This finding was first made by Clay Holden, in whose debt we are for this important discovery and the initial geometric constructions demonstrating the figure.

This correlation of the Monad to the sevenfold division of the circle indicates that an intimate relationship may exist between the metaphysical formulae of Dee’s Monad and Sigillum, sevenfold division being the very foundation of the formulae of the Sigillum.” [via]



Part III: The Circumference and the Hieroglyphic Monad in In Operibus Sigillo Dei Aemeth by David Richard Jones.

“The encoding of this connection is indicated by the relationship of the geometry of the Monad with that of the Sigillum. Note that the problem of constructing a regular heptagon sept-dividing (dividing a circle into seven equal parts) with the aid of a compass and a straightedge only without the aid of measurement has been a problem since classical times. So difficult a problem is it that no such formulation is provided in the Elements of Euclid, to which John Dee wrote his famous preface. A solution by Archimedes is preserved in Arabic, but was not rediscovered until 1927, and is notable even to its author/preserver for its lack of elegance.” [via]