Roger Burrows

Magnetically interactive substrates

One kind of the base sheet is printed in areas of magnetizable ink. Magnetizable ink is compresse... more

Teaching or amusement apparatus

A Design Method Based on Close-Packing Circles and Spheres of Multiple Sizes for Designers and Architects

A design method is presented that generates many new close-packing circle and sphere arrangements... more A design method is presented that generates many new close-packing circle and sphere arrangements of multiple sizes within tessellating tiles and prisms from which two and three dimensional polygonal shapes can be extracted. Introduction The story begins with a window design in the Sarghatmish Mosque Madrasa (1356 CE) in Old Cairo, Egypt, Figure 1, and an interpretation of the logic used to create the design on page 163 of “L’Art Arabe” (1879 CE) by Jules Bourgoin, see [1] and Figure 2(a). Bourgoin’s work focused on determining Islamic geometric methods used during the Abbasid Caliphate (750–1258CE in Baghdad and 1261-1517 CE in Cairo). Figure 1: Line drawings of the window in the Sarghatmish Mosque Madrasa (1356 CE) in Old Cairo. The Bourgoin method takes advantage of a near alignment of the lines of symmetry of four regular polygons – an octagon, a hexagon, a pentagon, and a heptagon – within a 45-degree right triangular tile that, when reflected and rotated, creates a tessellatin...

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A Design Method Based on Close-Packing Circles and Spheres of Multiple Sizes for Designers and Architects

A design method is presented that generates many new close-packing circle and sphere arrangements... more A design method is presented that generates many new close-packing circle and sphere arrangements of multiple sizes within tessellating tiles and prisms from which two and three dimensional polygonal shapes can be extracted. Introduction The story begins with a window design in the Sarghatmish Mosque Madrasa (1356 CE) in Old Cairo, Egypt, Figure 1, and an interpretation of the logic used to create the design on page 163 of “L’Art Arabe” (1879 CE) by Jules Bourgoin, see [1] and Figure 2(a). Bourgoin’s work focused on determining Islamic geometric methods used during the Abbasid Caliphate (750–1258CE in Baghdad and 1261-1517 CE in Cairo). Figure 1: Line drawings of the window in the Sarghatmish Mosque Madrasa (1356 CE) in Old Cairo. The Bourgoin method takes advantage of a near alignment of the lines of symmetry of four regular polygons – an octagon, a hexagon, a pentagon, and a heptagon – within a 45-degree right triangular tile that, when reflected and rotated, creates a tessellatin...

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Magnetic load supporting inks

Magnetically interactive substrates

Evolution and 'Bubble Logic' versus 'Tree Logic' The Dilemma

A friend of mine recently asked me if I could help him escape a logical dilemma within which he w... more A friend of mine recently asked me if I could help him escape a logical dilemma within which he was trapped. This dilemma followed the following line of reasoning: "As individuals we each have two parents, who each have two parents, who have two parents -and ongoing as an exponential growth, continuing until the beginning of human evolution. Following this line of thinking each of us would have more trillions of ancestors than we can imagine yet biblical wisdom has us as the decedents of just two human beings, namely an Adam and an Eve," see Figures 1 and 4.

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Space-Filling Golden Ratio Proportional Architecture

Bridges, 2018

Previously titled "A Dynamic Geometry for Designers, Artists and Architects." This dynamic geomet... more Previously titled "A Dynamic Geometry for Designers, Artists and Architects." This dynamic geometry provides a means to create golden ratio and other proportional two-and three-dimensional designs for applications in architecture, design and art. The geometry is dynamic and is based on circles or spheres that change size and position to form close-packing cells and clusters that fill space. Space filling lattices are generated from the cells and clusters by connecting contact points of the circles or spheres or by adding clipped tangent lines and planes at circle or sphere contact points. The lattices serve as 'ideation lattices' from which two-and three-dimensional forms can be extracted-of all sorts and of many types-limited only by the extent of one's imagination. The software so far used to generate the space filling lattices has been Rhino 3D and SolidWorks, so outputs can range from CNC cut components, or molds, to complete 3D printed, or 3D fused, forms. The author is currently developing a concept of micro and modular human habitats for high-density urban areas based on space-frames extracted from one of the geometry's lattices.

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Reconstructing Early Islamic Geometries

Bridges Linz, Austria 2019, 2019

An introduction to six early Islamic geometric methodologies that were used to create many two-di... more An introduction to six early Islamic geometric methodologies that were used to create many two-dimensional geometric surface designs that appear in windows, and on doors, walls, domes and minbars. These are reconstructions based on analysis and research of methodologies developed during the early years of Islam-particularly during Abbasid Caliphate (750-1258CE in Baghdad and 1261-1517 CE in Cairo) and also during corresponding periods in Persia, Morocco, Syria and Moorish Spain. The six methodologies presented are: (i) Grids, (ii) Tessellating Polygon Subdivisions, (iii) Rays, (iv) Close-Packed Circles, (v) Nesting Polygons and (vi) Modular Tiles. This paper also puts forward the idea that surface designs generated by these methods were not always intended to be purely decorational-they may have had meaning according to the logic of their design methodologies, their symbolic values, their 'perceptual' qualities and, possibly, their numeric values.

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Shape-Changing Polyhedra

Bridges 2016 Jyvaskyla, Finland, 2018

This is an introduction to shape-changing polyhedra that are defined as three-dimensional polygon... more This is an introduction to shape-changing polyhedra that are defined as three-dimensional polygonal structures that change shape and size and that create a completely new type of application opportunity. Shape changer geometries combined with new technologies will enable buildings to transform from one form into another, aircraft wings to flex, surfaces that will transform to change sound and light reflections, and much more. The primary approach presented here is to explore the domain of shape-changing polyhedra with flexibly connected polygons-connected in 2D and 3D arrangements where the 2D will transform into 3D and, in some cases, where 3D will transform into 2D. Media available for this presentation includes animations, movie clips, diagrams, illustrations, photos, models, simulations, and copies of, " Think 3D. "

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A Design Method Based on Close-Packing Circles and Spheres of Multiple Sizes for Designers and Architects

Bridges Conference 2018 Stockholm, Sweden, 2018

A design method that generates many new and unique close-packing circle and sphere arrangements o... more

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3D Thinking in Design and Architecture from Antiquity to the Future

Thames and Hudson, 2018

The product of decades of teaching and research, this unique and inspirational design resource pr... more The product of decades of teaching and research, 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. Explaining key principles that can be applied across all design disciplines, Roger Burrows 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.

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Evolution and 'Bubble Logic' versus 'Tree Logic' The Dilemma

A friend of mine recently asked me if I could help him escape a logical dilemma within which he w... more A friend of mine recently asked me if I could help him escape a logical dilemma within which he was trapped. This dilemma followed the following line of reasoning: "As individuals we each have two parents, who each have two parents, who have two parents-and ongoing as an exponential growth, continuing until the beginning of human evolution. Following this line of thinking each of us would have more trillions of ancestors than we can imagine yet biblical wisdom has us as the decedents of just two human beings, namely an Adam and an Eve," see Figures 1 and 4. Figure 1: Backtracking to ancestors of the past following a path of individuals Paths of Reason To help my friend, my reasoning explored evolutionary rather than biblical paths: Firstly, there was never a start with just two human beings. We could start with amoeba, but it might be simpler to start with apes and consider two processes in play where one is 'genetic evolution' and the other is 'skill development.' So, let's envision a number of apes, scattered over a geographical area, who have developed more survivable genetic-based and skill-based traits than others. Where such traits would not necessarily be the same but would nonetheless increase survival skills. Over time apes with survival advantages of some sort would mate with each other, mostly locally but sometimes at the distant fringes of their environment, with the result that some groups would dominate other groups-where dominating groups would have all sorts of variations of genetic-based and skill-based advantage. In time high survival skill apes would dominate the full extent of their environments with some interbreeding with 'lesser' apes and with some 'squeezing out' of less advantaged apes-one way or another.

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