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 […]
Girih Tiles on the
Just posted a video supplement to my 2020 Bridges Paper “Labyrinths Mysteries and Methods,” on my youtube channel rogerburrowsimages https://www.youtube.com/watch?v=z5td10JrcrU. The link to the paper is http://archive.bridgesmathart.org/202… The paper and the supplement present five methods for constructing labyrinths that can be used to create ancient labyrinths or used to create new ones as far as […]
“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 four […]
“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 labyrinths […]
“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” 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 […]
