Saturday, October 22, 2016

Geometric Harmony

Many living organisms, inanimate objects, and geologic formations have polygonal shapes. Polygons are a chain of straight segments that form a closed chain like the hexagonal cells of honeycomb:
Hexagonal paper wasp honeycomb
by coniferconifer

The pentagonal shape of a sweet potato flower:

The variably-sided segments of desiccation cracks:

Polygonal desiccation cracks in sewage plant sludge
by Hannes Grobe

Our observable universe seems characterized by a curious preponderance of geometric forms.

Seventeenth century astronomer and mathematician Johannes Kepler wrote of the harmony and congruence in geometrical forms and physical phenomena in The Harmony of the World (Harmonice Mundi).

Archimedean polyhedra used by Kepler in Harmonice Mundi

To me it seems that diversity in things is created from nowhere other than matter, or from occasions caused by matter, and where there is matter there is geometry.

— Johannes Kepler, 1601
In The Nature of Order twentieth century architect and design theorist Christopher Alexander writes of the relationship between life and space.

Alexander argues that life is not merely in space, but of it. He proposes that the nature of space accounts for the occurrence of life.
I believe that all centers that appear in space - whether they originate in biology, in physical forces, in pure geometry, in color - are alike simply in that they all animate space. It is this animated space that has its functional effect upon the world, that determines the way things work, that governs the presence of harmony and life.
Christopher Alexander