Since ancient times artists and architects have used various geometrical and mathmatical properties in their work. You could take some examples simply by observing the refined use of the proportions by architects from ancient Egypt, Greece and Rome or Renaissance artists like Michelangelo, Da Vinci or Raphael. Astonishly, many of these properties and mathematical developments are also present in nature.
The animation above begins by presenting the Fibonacci Sequence. The second part of the animation introduces the concept of Golden Ratio by constructing a Golden Rectangle. In the third part a less known concept is presented: the Voronoi Tessellations, also called Dirichlet Tessellation.
These geometric formations are based on a distribution pattern that is easily recognizable in many natural structures, like the wings of some insects or these small capillary ramifications in the leaves of some plants. To further explores natures mathmatics there is a TED talk by Arthur Benjamin that explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series below: