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The Intimate Relation between Mechanics and Geometry

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Radically novel materials change shape by 100s% following changes in temperature or illumination. Shape change, rather than simply that of volume, when imaginatively arranged can induce intrinsic curvature change in initially flat spaces. The intimate connection between differential geometry and mechanics comes into play and suggests ways of exploiting light-induced curvature of space for new mechanics paradigms.

I will give, with demonstrations, examples of the materials involved and of the geometry arising. These solids can apparently solve the map-maker’s problem of resolving planes with curved space. I will say how this unique property might be exploited.

This talk is part of the Cambridge University Physics Society series.

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