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 pine-cone, 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