## FIRE ALTARS OF THE VEDAS – A LOGICAL PUZZLE FROM ANCIENT INDIA

“3D Thinking” Pages 67 to 72: Vedic Fire Altars present a logical puzzle for those building them. Firstly, the surface area has to be in direct proportion to the height of the individual whose task it is to construct the altar. Secondly, there is to be a precise alignment of the altar with the fourContinue reading FIRE ALTARS OF THE VEDAS – A LOGICAL PUZZLE FROM ANCIENT INDIA

## LABRYNTHS MYSTERIES and METHODS

“3D Thinking” Page 32 Neolithic Geometries: Labyrinths are constructed with a single path that winds forwards and backwards, multiple times, before arriving at a central point. The oldest surviving labyrinths appear as Neolithic and Bronze Age rock carvings – a petroglyph labyrinth in Usgalimol, India has been estimated to be 10,000 years old. By the time of the middle ages labyrinthsContinue reading LABRYNTHS MYSTERIES and METHODS

## Geometry Ancient Egypt – Pyramid Proportions

“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 squareContinue reading Geometry Ancient Egypt – Pyramid Proportions

## 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 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

## 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 toContinue reading Geometry New Golden Ratio Icon

## 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

## Nancy Stetson’s Art Studio, Boulder, Colorado

We went to visit an old friend of mine, Nancy Stetson, in Boulder, Colorado, two weekends ago. About thirty-five years ago Nancy asked me if I would design an art studio, to be built on the foothills just above Boulder. This I did using one of the geometries that I had developed and that generatedContinue reading Nancy Stetson’s Art Studio, Boulder, Colorado