This will be my only post for 2021 as I’ve been working on my new book all to do with visualization and imagination in the arts and architecture; through time (almost complete). This post is from my 2020 paper given at Bridges Math/Art 2020. Two animations and one illustration sequence. The Nazca giant-geoglyph spirals that […]
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“3D Thinking” Page 74 to 87: The slope ratios, dimensions, construction, and alignment methods, of the Pyramids of Ancient Egypt: THE SLOPES OF THE PYRAMIDS OF EGYPT Given the whole number traditions of ancient Egypt one would expect the slopes of the pyramids to be in whole number proportions too. Whole number grids of square […]
“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 from […]
“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 numbers […]
“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 the […]
“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) a […]
“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 areas […]
“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 of […]
“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
