Math CentralQuandaries & Queries


Question from cleo, a teacher:

what geometric ideas can you find in the woods

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

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