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Holistic Geometry – The Key of Proportions

When I told myself that I have rediscovered “The Holistic Geometry”, I started from the prerequisite that there really was a time when it used to be known. I would place its existence either in ancient Egypt or in Pytagora’s times and a few centuries after that. I consider that this form of approaching geometry has been lost in the course of time. Euclid’s “elements” come, as if to strengthen once more its existence in those times.  Everything started about ten years ago, when, while residing in Madeira, Portugal, I started, under the influence of Matila Ghyka’s attractive book, to look for elucidating the problem of proportions. Intuition made me take the road open by the American Jay Hambidje with his theory on “Dynamic symmetry”. Now I can say that only Holistic Geometry can clarify the problem of proportions, I might say that it almost identifies with it.

By definition, (holistic) geometry is a “continuum – immovable”. Human thought being discursive, cannot analyze that immovable – continuum except by destroying and cutting it into fragments or elements lacking life or even sense. The Whole will no longer be the sum of its elements.  It is only the consciousness that can do that. It is in a straight connection with the Universal Intelligence, with The Logos.
Approaching Euclidian space in this manner simplifies and clarifies about everything that is important to be known from this domain of geometry. And if the problem of proportions has also found itself a valid solution, then the entire toil of nights and days along so many years, was worth it.

According to Descartes, “The Science of Proportions” represents the true “Mathesis Universalis”  – “everything boiled down to order and measure” he said.
“Euclidean space is nothing but a group of transformations”. H. Poincare.
“The structure of things, a copy of the model perceived by the Logos as a result of the Idea and the Number, constitutes the sole reality.” Nicomachus of Gerasa

The System
– The graphic constructions are executed according to geometrical principles (through construction)
– the construction of  structure,  especially the one generating geometrical proportions, of symmetry or analogy
– the principle   “Application of areas”  (“supraposition”, “adjoining/ juxtaposition”, lat. “adplicatio”)
– the implementation of the geometrical environments, theoretically never-ending, within the structure.

System characteristics

“symmetry” or “commodulatio” is obtained

– the plane is conferred a perfectly organic feature (the interconnection between the parts and the whole, on the one side, and between the parts themselves is achieved perfectly)
– the generation of a never-ending range of proportions (especially “dynamic rectangles”) and of the proportions, respectively
–  the consequence will be a reiteration of the  fundamental shapes, but on different scales
– the invariants which characterize any structure or group of transformations are to be found as  geometrical loci within the totality of the points in the plane (we refer to curves, circle, ellipsis, hyperbole, parabolas, logarithmic spirals, cissoids, etc.)
– these invariants are a correct result of the structure and they participate graphically to the continuous amplifying or division of the value system.
– under the influence of the number, the Euclidian surface is divided and fragmented endlessly, without a change of the topic; the surface seems to be rippled by curve fascicles, etc. rendered evident by means of a dot like system; it seems that the entire Euclidean surface is a mere geometrical locus.

The  Cathedral