Whirling Dervish Door Geometry

This Seljuk period door dates from 13th-century Anatolia and stands as a possible example of a use of numeric values to communicate a message. The door’s design is based on a close-packing arrangement of circles within a pentagon. The two primary numbers featured are “5” and 10″ – a number combination that occurs frequently in Islam but in this case the door was to a dancing hall for the whirling dervishes. Through the ABJAD system the numbers seem to describe the dance: (i) 10-5 Astronomy, cry for calling camels for water. To prepare, to arrange, thing agreed upon. (ii) 50-5-10 To loose the mind. Receive a blessing, on the right side, the right hand. (iii) 100-5 Cry to excite horses, they thronged at the water. Three stars in Orion, fifth mansion of the moon. (iv) 5-100 Top of the head. Summit of the body. Translation: Edward Lane’s 1876 root dictionary. The dervishes rotate like the stars in the night sky. Their right hand faces upwards and their left faces down. They wear tall hats enhancing the summit of their bodies…



Arabian Designs – Close-Packing Circle Dynamics

Using close-packing circles to create surface designs, during the early years of Islam, requires a method to generate different close-packing circle arrangements. The dynamic sphere geometry provides such a method. Applying the geometry, starting with a 5-circle arrangement within the unit triangle of a square, generates many arrangements including the arrangement (8th in the sequence) that was used to create the window design of the 1356CE Madrasa of Amir Salf al-din Sargatmish in Old Cairo, Egypt. Basically the method requires algorithmic steps where circle sizes and positions are changed in a step-by-step fashion. Once one understands the dynamics of the geometry then looking at the Madrasa window in old Cairo becomes a dynamic experience that couples with the numerology of the window itself, for example, 5, 6 and 7 (سنع; نزخ; نوذ) – a repository, a place of wealth. Connecting circle contact and center points with rosettes and straight lines will create surface designs or lattices of which some will have been used in the past.


Arabian Designs – Close-Packing Circle Method

The animation below shows the Arabian “close-packing” circle method that was used to create the window design of the 1356CE Madrasa of Amir Salf al-din Sargatmish in Old Cairo, Egypt. The design method dates back to the Abbasid period – a time of great creativity. The development starts with (i) a photo of the actual window and then follows with line drawings (ii) a line drawing of the window (iii) the rosette design (iv) the close-packing circle construction with the rosette development (v) the close-packing circle construction with circle centers connected (vi) the close-packing circle construction and tangent polygons with internal radii. Where the lattices of the last two drawings are “Altair Designs,” and both function as “perceptual lattices.”


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.



Arabian Designs – The “Ray” Method

An example of the Ray Method – one of the six primary methods used to create Arabian designs during the early Islamic period – during the Abbasid Caliphate 566-653CE. In the animation one arm of a “10-Ray” is used to position a “6-Ray” – then on the intersection of one of the arms of the 10-Ray and the 6-Ray a “9-Ray” approximately fits. The method was used to generate designs based on number sequences that corresponded to letters and words using the ABJAD system – in this case the numbers 10, 6 and 9. See my paper on the subject, “Six Arabian Geometries” also the “Early Islam” chapter in my new book to be published by Thames and Hudson in April 2018, “3D Thinking in Design and Architecture from Antiquity to the Future.”

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.  In 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.

3D Thinking in Design & Architecture – April 2018

3D Thinking – Geometry culture and design throughout human history – April 2018

Will be available internationally through Amazon, Thames & Hudson UK and USA. UKP 39.95. 328 pages, over one thousand illustrations and photos.

This unique and inspirational design resource presents a history of the intimate relationships between geometry, culture and design throughout human history, from the Neolithic period through the Indian, Egyptian, Babylonian, Chinese, Greek, Celtic, Islamic, pre-Columbian and Renaissance cultures, to the present and the possible future.

Explains key principles that can be applied across all design disciplines, Reveals fresh insights into how geometry as a visual language has evolved to meet our needs, initiated new technologies, solved problems and changed the way we think about the world around us.

  • An essential sourcebook for design and architecture students, professionals, and general interest readers.
  • Covers humankind’s approaches to design and architecture across the entire range of human history and culture.
  • Stimulates new ways of thinking about the pressing design challenges of our present and future.
  • Illustrated with over one thousand specially created diagrams and artworks.


Mind Doodles

Mind Doodles are visual puzzles – the product of various types of logic developed by cultures past and present. Each design has been selected to stimulate your visual perception or to challenge your logic.

The book is sized like a journal but its objective is to stimulate ideas, to provide a platform for creativity, to provide space for idle thoughts and concepts; a book to personalize and to keep over the years. The book is for creative people and thoughtful people, for people who are interested in the visual ideas of the past and the present: for designers, artists, students, architects, mathematicians, historians, and for the idly curious.

Published by Park City Publishing and available at parkcitypublishing.com – go to the menu item BOOKSTORE.