PRESENTATIONS DERIVED FROM “3D THINKING IN DESIGN AND ARCHITECTURE FROM ANTIQUITY TO THE FUTURE.”  To be published by Thames and Hudson Ltd April 2018 and available for pre-order through Amazon USA, UK and other major distributors.

Presentations are multi-media with photos, illustrations, animations and movie-clips. Presentations include visual overviews of associated cultures – art, design, architecture, astronomical practices, local knowledge and traditions, etc.

1: THE GOLDEN RATIO – A DIVINE PROPORTION? The Golden Ratio – a ratio that, in popular culture, appears in the Great Pyramid of Giza, the Parthenon, and the paintings of DaVinci. It is a fact that the Golden Ratio lies at the end of a convergence with the Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21,..) – a sequence that appears to follow natural growth patterns in plants and many natural events – so does that make it a divine proportion? Does it qualify? Are popular ideas about the Golden Ratio correct or not?  How does the Golden Ratio compare with the divine proportions of Vitruvius and the Pythagoreans, as well with the divine proportions of other cultures? This presentation will raise the subject of what might be considered as a ‘divine proportion,’ and will also reveal for the first time properties of the Golden Ratio that are unknown and that might give it an unexpected advantage. 1st Presented at the Leonardo Museum March 2016.

2:  THE FUTURE OF ARCHITECTURE. “Looking to the future of Architecture we have many amazing opportunities with the possibility of, ‘drive-up,’ massive 3D printers that can create fused silicon, metal, and plastic structures; new types of concrete, bonded wood, new nano- and micro- structured materials; even bio-forming processes of different types. We stand at a threshold where almost any conceivable shape and structure is possible – incredibly cantilevered, cellular, floating, shape-changing, etc. We also have the mathematics and software to generate a huge variety of internal and external forms – with creative transitional spaces. Question is, ‘what will drive new architectural forms?’ Will it be extreme economic constraints, more rectangular boxes – with some high profile sculptural exceptions. Or will it be new types of structure designed to enhance the human experience? Historically there has been some precedence for the latter but not much of an empirical basis and there appears to be very little research into the human impact of, ‘architectural space,’ other than studies in color, light, and ergonomics. So what should the empirical basis be?” Presented at the Leonardo Museum April 2016.

3: SHAPE CHANGING POLYHEDRA. This is an introduction to shape-changing polyhedra – defined as three-dimensional polygonal structures that change shape and size and that create a completely new type of application opportunity. A number of shape-changing geometries are already under development with prototypes that have the potential to make shape-changing buildings, aircraft wings that can flex, two dimensional surfaces that can transform into three dimensional robots, and much more. The geometry presented here is the geometry of shape-changing polyhedra composed of flexibly connected polygons – connected in 2D and 3D arrangements where the 2D will transform into 3D and where 3D will transform from one form into another. Presented at the Bridges Conference August 2016, University of Jyvaskyla, Finland.

4: A DYNAMIC GEOMETRY FOR DESIGNERS, ARTISTS & ARCHITECTS. The ‘Dynamic Geometry’ provides a means to generate new types of two- and three-dimensional form for possible applications in design, art and architecture. 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 clipping tangent lines and planes at circle or sphere contact points. The structures 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. Paper to be submitted for a presentation at Bridges 2018 in Stockholm.

5: ARABIAN GEOMETRIES. This is an introduction to concepts that underlie the six main geometric design systems developed during the Abbasid caliphate of the Muslim Empire. The approach aims to reveal design methodologies that can stand independent of the ‘Islamic’ shell that surrounds them – and hopefully will serve as clearer start-points for new concept development. 8th to 13th century CE Arabian geometric design systems evolved due to needs – physical, cultural and philosophical. Designs were often rendered in symbolic form where, for example, the use of rosettes was common, however the methodologies underlying the designs stand independent of any symbolism and can be used creatively where core design lattices can be generated and then serve to generate derivative designs and applications.  Methodologies of the early Islamic period can be described as: (i) Grids; (ii) Tessellating Polygon Subdivisions; (iii) Rays; (iv) Close-Packed Circles; (v) Nesting Polygons; (vi) Modular.  Layered over the design methodologies are specific color pallets and also function and sequencing. Function can include acoustical, transitional, psychological impact, and even messaging (through the ABJAD number-letter system). ‘Sequencing,’ is the order within which the designs are experienced.

6: THE PYTHAGOREANS. This is a presentation of a number of Pythagorean geometrical concepts with speculations about how they might have been further developed at the time of the ancient Greeks even though not much in the way of evidence survives. The intention of the presentation is to show that ancient ideas can still inspire new concepts for present day and future applications. Featured in the presentation will be a review of (i) The Pythagorean theorem and how Euclid’s proof and comments compare with other proofs and concepts particularly a “self-evident” ancient Chinese proof; how the Pythagorean theorem can be interpreted in terms of dynamic circles and how circle configurations cross-over to a unique and unknown close-packing, ‘Golden Rectangle,’ sphere arrangement and its generated tessellating lattices; how Euclid’s ‘mean and extreme’ ratio (‘golden ratio’) also cross-links with the ‘Golden’ close-packing sphere arrangement and the Fibonacci sequence with something of a realistic perspective. (ii) How Platonic and Archimedean solids can be extended and combined and how they might have been used to investigate the emotional / physiological / psychological impacts on men and women of 3D spatial structures (refencing the works of Vitruvius) with some links to the pentatonic scale. (iii) How Pythagorean tessellations combined with Euclidian statements anticipate the non-periodic tilings of Roger Penrose and Islamic periodic tiling designs.

7: LABYRINTHS MYSTERIES AND METHODS. This is an introduction to the mysteries and methods of labyrinths from their Neolithic past and then across time and space through to the present and possible future. The first labyrinths appear as petroglyphs and then more famously in Crete, in ancient Rome, and then as far afield as on islands off the north coast of Russia, the Americas, Scandanavia, and India – and in cathedrals of the 12th and 13th centuries CE. The ‘why,’ and ‘how,’ are the key parts of this presentation. The ‘why,’ ranges from mere doodling to ancient Earth concepts of energy and passages to the underworld, to solar and lunar calendars, to paths for dancing, meditation, and chanting. The ‘how,’ is presented by way of various methods for generating labyrinths from the ancient to the more modern: (i) Key; (ii) Grid; (iii) Modular (iv) Switch.

8: GEOMETRIES OF THE PRE-COLUMBIAN AMERICAS. This is an introduction to the geometries of the Pre-Columbian Americas with an overview of astronomical and architectural practices and concepts. The first humans appear to have arrived sometime after the last ice-age, possibly 14,000 BCE, expanding and diversifying into tribal groups numbering in their thousands with an equivalent number of languages – possibly evolving from a core group of about fifty. Many civilizations and cultures  arose throughout the Americas including the Pueblo, Adena, Hopewell, and Mississippian cultures in the North, the Aztec and Mayan civilizations in middle America, and the Nazca, Muisca, and Inca cultures and civilization in the South. Given the diversification a great number of architectural, geometric, astronomical, and numeric methods and practices developed and many are presented with the view of promoting discussions.

9: INDUS VALLEY GEOMETRIES. Geometries develop at a pace to match social needs and are shaped by local environments, knowledge and culture. The Harappan city state developed some 5,000 years ago in the valley of the river Indus and with it the development of rectangular and circular architectural forms, standardized measurements and building materials, plumbing, arithmetic, astronomical practices, script, art and much more. The Harappans worshipped a multiplicity of gods – gods of the earth, water, air, fish, buffalo,…There was a belief that the quality of human behavior was monitored by the gods – that focusing ones behavior and communicating that focus to the gods would keep an individual on a path towards perfection. This belief manifested itself in the rituals of fire altars, the construction of which necessitated a knowledge of mathematics and astronomy. The practices and knowledge of fire altar construction are communicated in the Vedas – stories originally past down the generations by word of mouth and then through Vedic Sanskrit – an ancient numeric vowel (16)-consonantal (36) script. Practices include basing measurements on the person building a fire-altar and not on an idealized human as in Western culture; maintaining areas no matter what the shape of a fire altar might be – a falcon, a square, or a circle.

10: 3D THINKING – An exploration of visual logic through time and space: The foundations, forms and patterns in architecture, design and decorative arts throughout the world have been deeply influenced by the geometries of past cultures. From the first path-like doodles on cave walls through to the higher abstractions developed to make accurate measurements and predictions, the three-dimensional forms we design and build are dependent upon available materials, human needs and the limitations of our imaginations. An overview of the history of the intimate relationships between geometry, mathematics 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, and 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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