Here is a great video making the rounds showing the inherent beauty of mathematics in the natural world.  Throughout ecosystems and in natural objects you see these patterns repeated over and over.  This video does a great job illustrating the math behind it, starting with the Fibonacci sequence, then the Golden and Angle Ratios, the Delaunay Triangulation and Voronoi Tessellations.

Thanks to BoingBoing for the tip!  See also Nature by Numbers.