The language of Symmetry allows us to describe not only the rotation and translation of shapes in space, but also the shape of those transformations themselves. Quite apart from whatever shapes are being transformed, we can talk about rotation itself as a thing with a definite form.

The exploration of such dynamic forms can give us deep insights about the nature of physical reality and they also have a startling beauty all of their own.

These ideas stretch our everyday sense of space and shape, but spatial intuition can be exercised through use and play. Engaging with the geometry and topology of 2, 3 and even 4 dimensional spaces can enhance the mental facility to manipulate imagined objects. Increasing spatial ability in this way can open up thrilling new vistas and could be useful for artists, architects, designers, sculptors or anyone who has to deal with space in a creative way.

Daniel studied at the Architectural Association and has worked for Arup’s Advanced Geometry Unit (AGU). He has a particular fascination with geometry and the nature of space which he explores through the making of experimental structures, sculptural forms, toys and puzzles. Using physical models, 3D architectural modeling software and custom written programs, he takes deep and abstract concepts from mathematics and physics and manifests them so they can be appreciated visually and intuitively.

The talk will cover a range of topics from tensegrity to topological torsion, Chirality to complex numbers, quasicrystals to quaternions, fluid flows to folding spaceframes, spinors to stereographic projection, loxodromes to logarithmic spirals, Möbius transformations to minimal surfaces, and Daniel’s personal approach to the role of geometry in architecture. All copiously illustrated with animations, models, toys and puzzles.


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