Roger Penrose - Forbidden Crystal Symmetry in Mathematics and Architecture

Explore a fascinating lecture on the mathematical principles behind "forbidden symmetry" and non-repeating patterns in design and architecture. Delve into the world of crystallographic symmetries, including the mathematically possible 5-fold, 8-fold, 10-fold, and 12-fold "almost" symmetric patterns that deviate from exact symmetry by an arbitrarily small amount. Discover the beauty and applications of these patterns in architectural designs worldwide, with a focus on the novel version of "Penrose tiling" used in the approach to Oxford's new Mathematics Institute. Learn about the connection between these patterns and quasi-crystalline materials in atomic structures, which led to a Nobel Prize in chemistry. Examine various examples of forbidden symmetries in architecture, from ancient Islamic art to modern buildings, and gain insight into the mathematical underpinnings of these intriguing designs.