Tag Archives: Geometry

Königsberg Bridges

Background The great Swiss mathematician Leonhard Euler, who had been asked by the Mayor of Danzig to provide a solution to the Königsberg Bridge problem, sent him this disdainful reply: “. . .  Thus you see, most noble Sir, how this type of … Continue reading

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William Tutte’s Hidden Past

If William Tutte is remembered at all by architects, it is for his contribution to solving the problem of Squaring the Square . (Tutte 1958) A solution using Graph Theory and Kirchhoff’s Laws for electrical flow in wires that was subsequently used in Philip … Continue reading

Posted in Architecture, Design Methods, Geometry, Logic, Tiling | Tagged , , , , , , | 3 Comments


The school report of Emily, our 4 year old grandchild, said that she could subitise up to the number 6, and I had no idea what this meant. Subitising is a technical term that comes from the Latin root subito … Continue reading

Posted in Aesthetics, Architecture, Brain Physiology, Design, Design Methods, Enumeration, Geometry, Randomness | Tagged , , , , , | 1 Comment

Smartgeometry 2013

The tenth annual smartgeometry event has just finished in London, and was held at the Bartlett School of Architecture. Previous years’ events have been held at Troy, Copenhagen, Barcelona, New York and San Francisco with institutions bidding for the privilege of hosting … Continue reading

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Visual Thinking

I have recently become interested in visual thinking, probably because I like making arguments visually but also as a result of having encountered problems in producing simple easy to understand diagrams. Diagrammatic Illustrations The minimal (graphics only) version above contains … Continue reading

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Wang Tiles and Turing Machines

Wang pointed out that it is possible to find sets of Wang tiles that mimic the behaviour of any Turing Machine (Wang 1975). A Turing machine can compute all recursive functions, that is functions whose values can be calculated in … Continue reading

Posted in Aperiodic Tiling, Architecture, Geometry, Tiling, Turing | Tagged , , , , | 22 Comments

Wang Tiles and Aperiodic Tiling

Wang originally conjectured that no aperiodic tilings could exist. Wang was interested in the decidability of the Tiling Problem; it is said to be decidable if there exists an algorithm which will yield a solution for any given set of prototiles … Continue reading

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Aperiodic Tiling

This closely follows “Tilings and Patterns” (Grünbaum and Shephard, 1987), but uses coloured diagrams rather than their monochrome ones. In some ways this is simply a catalogue of aperiodic tilings, their various forms and some indication of their uses, but my interest … Continue reading

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Periodic and Non-Periodic Tiling

The concepts of periodic and non-periodic tiling are defined so as to clearly distinguish them from aperiodic tiling; the subject of a future post “Aperiodic Tiling”. Informally a tiling (of the 2D Euclidean plane) is a collection of subsets of … Continue reading

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Haptic Bedside Lamp

I had surprisingly forgotten about this haptic lamp that actually sits in one of our bedrooms. We originally came across them in a smart B+B in Arboyne and initially were flumoxed by them. The clue to its use is on the … Continue reading

Posted in Design, Geometry, Haptic Objects, Products | Tagged , , , | 3 Comments