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.

Intro
Crystallographic symmetry
Geometric symmetry
Why doesnt the theorem work
Features of the pattern
Structure of the pattern
Subtlety
Ancient Islamic art
Johannes Kepler
Kepler pentagons
Kepler
Tile shapes
Pentagons
kites and darts
non periodic arrangements
Rhombus pattern
Mauri pattern
Local assembly
PowerPoint images
Atomic arrangements
Japanese architect
Storyhole
The Science Centre
St Johns College
Helsinki
Stoneybrook Simon Center
Chemistry Department
Carleton University
Allahabad India
Transbay Transit Area
Park
Railway station
Wadham College
Pentagon
Rings
Rhombus
Floral arrangement
Latest progress
The Radcliffe Observatory