With an experienced eye  one sees geometry almost everywhere. Note that I have a broad definition of 'geometry'
 the way plants spread out their leaves to optimize exposure to sun (sometimes with opposite branches, sometimes with alternating branches and leaves, sometimes with spirals) ...
 the pattern of scales on a pinecone, related to Fibinocci numbers;
 the ways in which roots follow a 'fractal' branching pattern to optimize access to water and nutrients;
 the symmetry that balances the forces on a tall tree;
 the balance of compression members in limbs, and layers on the top of the limbs which are good for tension, so that the limbs stay angling up;
 bilateral symmetry in most animals  this is geometry / efficient reuse of design components;
 the bilateral symmetry of most leaves of trees  and most flowers;
 the geometry down in the biochemistry of plants and animals (why do all plants and animals produce the same single form of Vitamin E  not the other 7/8 ths of the patterns a chemist produces)? This geometric distinction (Chirality) is why some bottles of Vitamin E say 'natural source'!
 the geometry of patterns that appear throughout Nature  see books like Symmetry in Nature; and D'Arcy Thompson's classic On Growth and Form.
 the geometry of houses' shelters that animals build (including birds);
 the geometry of patterns in rocks, on the beach, ... .
 the geometry of fruits
I am sure there are more  and a simple google search with Geometry in Nature produced 12 million hits!! The top ones were just pictures ... .
Walter Whiteley
York University
