Is One Rectangle More Beautiful Than All the Others?

Mathematics Education
Art and Environment
Edward Hessler

Golden ratio, via Pixabay.

BBC Radio 4 and The Open University produced an animation about a ratio that results in what became a fascinating irrational number. It has attracted mathematicians since Kepler for its putative manifestations in architecture and the natural world.

The animation is here and is less than two minutes. It focuses only on this quality of some rectangles but touches on a few others.

Some examples in which this pattern is inferred is the design of the Parthenon, the spiral of the Nautilus shell, its use by Renaissance artists such as Botticelli, Da Vinci and Michelangelo, the spirals seen in nature such as the flower head of a sunflower, pine cones, pineapples, etc.

For criticism if whether this mathematical pattern is common in the designed and natural world see here.