The geometry of art and life, Ghyka M., 1977

The geometry of art and life, Ghyka M., 1977.

   It is not generally suspected how much the above pronouncement of Plato—or in a more general way, his conception of Aesthetics—has influenced European (or, let us say, Western) Thought and Art, especially Architecture. In the same way that Plato conceived the “Great Ordering One” (or “the One ordering with Art,”) as arranging the Cosmos harmoniously according to the preexisting, eternal, paradigma, archetypes or ideas, so the Platonic — or rather, neo-Platonic—view of Art conceived the Artist as planning his work of Art according to a preexisting system of proportions, as a “symphonic” composition, ruled by a “dynamic symmetry” corresponding in space to musical eurhythmy in time. This technique of correlated proportions was in fact transposed from the Pythagorean conception of musical harmony: the intervals between notes being measured by the lengths of the strings of the lyra, not by the frequencies of the tones (but the result is the same, as length and numbers of vibrations are inversely proportional), so that the chords produce comparisons or combinations of ratios, that is, systems of proportions.




Proportion in Space and Time.
The notion of proportion is, in logic as well as in Aesthetics, one of the most elementary, most important, and most difficult to sort out with precision; it is either confused with the notion of ratio, which comes logically before it, or (especially when talking of proportions in the plural) with the notion of a chain of characteristic ratios linked together by a modulus, a common sub-multiple; we have then the more complex concept which the Greeks and Vitruvius called “Symmetria ” and the Renaissance architects, “Commodulatio” Let us start from the definition of ratio.

Contents.
CHAPTER I PROPORTION IN SPACE AND TIME.
CHAPTER II THE GOLDEN SECTION.
CHAPTER III GEOMETRICAL SHAPES ON THE PLANE.
CHAPTER IV GEOMETRICAL SHAPES IN SPACE.
CHAPTER V THE REGULAR PARTITIONS ON THE PLANE AND IN SPACE.
CHAPTER VI THE GEOMETRY OF LIFE.
CHAPTER VII THE TRANSMISSION OF GEOMETRICAL SYMBOLS AND PLANS.
CHAPTER VIII GREEK AND GOTHIC CANONS OF PROPORTION.
CHAPTER IX SYMPHONIC COMPOSITION.



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