Divine Proportions


Ideas of “Divine Proportions” originated in the distant past. For the Pythagoreans whole numbers resonated throughout the cosmos in sacred music, in geometry and in number. For the Harrapans of the Indus Valley they found expression in fire altars of different shapes but of constant areas but also in the Vedas and in numerology. For the ancient Egyptians nighttime star charts heralded the arrival of the decan stars and whole numbers determined the proportions of almost every artistic and structural form. For DaVinci whole number divisions determined the divine proportions of human form. For Le Corbusier, the architect, they represented harmonious proportions in architecture. The illustration shows: Egyptian Star Chart (whole number); Egyptian drawing grid (whole number); Indus Valley Uttaravedi Sky Altar proportions (whole number and whole number divisions of fire-altar bricks); DaVinci/Vitruvian/ancient Greek (whole number); Le Corbusier character combined with a Golden Sphere cluster (Spheres in 3D golden ratio proportions generated by the Dynamic Sphere Geometry). Ancient Egyptian and Greek based on idealized humans where the Uttaravedi is based on individual humans. In the examples shown all measurements are from the middle of the forehead at the hairline – the “third eye” of Hindu belief.

 

 

Architecture Ideation Lattices 2

The drawing shows an example of how an “Ideation Lattice” is derived from the “Dynamic Sphere” geometry – and then how an architectural structure is extracted from the lattice. ┬áIn this example, connecting sphere centers creates the lattice. The sphere packing is the “Golden Ratio” packing. Software is Rhino 3D. Once the lattice is generated three-dimensional forms of all sorts can be extracted from it – where the forms will all be within the Golden Ratio. See my paper on the subject, “Dynamic Geometry,” also a chapter in my upcoming book to be published by Thames and Hudson April 2018 “3D Thinking in Design and Architecture from Antiquity to the Future.”

Architecture Ideation Lattices 1

“Ideation lattices” are three-dimensional latticed generated by the “Dynamic Sphere Geometry” to stimulate “visual logic” and creativity. They are the three-dimensional equivalent of “Perceptual Patterns.

Form extracted from an ideation lattice generated by the dynamic sphere geometry

New Golden Ratio Icon

This new rogerburrowsimages.com icon shows the relationship between Le Corbusier’s ‘man’ and the “Golden Sphere” packing generated by the author’s “Dynamic Sphere” geometry. The packing generates three-dimensional “ideation lattices” from which design, art, and architectural forms can be extracted. As much as DaVinci’e “Vitruvian Man” represents a “whole number” proportionate system that dates back to ancient Greece and ancient Egypt the new icon represents a three-dimensional, “Golden Ratio” proportionate system.