A Geometry of Early Islam – Nesting Polygons

“3D Thinking” Page 190, 191: There are a number of Islamic design methodologies of which the “Nesting Polygon” method is one. The method places an arrangement of polygons within a polygon and continues infinitely placing the same but scaled arrangement within each polygon as it appears. The method was used to generate a lattice fromContinue reading A Geometry of Early Islam – Nesting Polygons

A Geometry of Early Islam – ABJAD, Circles and a Door

“3D Thinking” Pages 175 to 177 Islamic 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 the Islamic “close-packing circle” method of design – in this case an arrangement of close-packing circles within a pentagon. The two primary numbersContinue reading A Geometry of Early Islam – ABJAD, Circles and a Door

A Geometry of Early Islam – The Dynamic Circle Method

“3D Thinking” Pages 187, 274: 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 theContinue reading A Geometry of Early Islam – The Dynamic Circle Method

A Geometry of Early Islam – The Circle Method and a Window

“3D Thinking” Page 187: 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) aContinue reading A Geometry of Early Islam – The Circle Method and a Window

Geometry Divine Proportions

“3D Thinking” Pages 67, 75, 77, 210 to 213: 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 areasContinue reading Geometry Divine Proportions

A Geometry of Early Islam – The “Ray” Method

“3D Thinking” Pages 183 to 186: 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 ofContinue reading A Geometry of Early Islam – The “Ray” Method

Geometry Architecture Golden Ratio Proportions

“3D Thinking” Pages 280 to 289: The drawing shows an example of how a Golden Ratio “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. SoftwareContinue reading Geometry Architecture Golden Ratio Proportions

Geometry Architecture Dynamic Sphere Lattices

“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

3D Thinking in Design & Architecture – April 2018

“3D Thinking in Design and Architecture from Antiquity to the Future” – Thames and Hudson – April 2018. Amazon UK; Amazon USA; Waterstones UK. UKP 39.95. 328 pages, over one thousand illustrations and photos. INDEX: Visual Logic 14. Neolithic Geometries 32. The River Cultures 58. The Americas 106. The Pythagoreans 124. European Tribal Geometry 160. Geometries ofContinue reading 3D Thinking in Design & Architecture – April 2018