Design and Mathematics
There are so many places where mathematics can be found in nature and much of our inspiration as designers comes from and is an imitation of nature.
Axes of symmetry can be traced in the petals of a flower and patterns such as a star are known to stand out.

Bees phenomenally store their eggs and larvae in hexagonal wax cells. Hexagons fit closely together, avoiding wasted space in the beehive.

People use geometry to divide up their land. Property lines can be seen in the shapes of squares and rectangles when viewed from above.

A perfect circle and be seen during an eclipse where the relationship of its circumference divided by its diameter equals pi.

Fractal shapes are form repeated at every scale. Frost covered branches are a beautiful example of this relationship.

The chambers of a nautilus shell are an example of the Fibonacci spiral.

A golden ratio is often found in human architecture and plant life. A Golden Spiral, something similar to the Fibonacci spiral can be found in the golden seeds of a sunflower – starting from the center and working its way outwards.

And finally – infinity - something that is almost incomprehensible for the human mind.

The findings of math among nature are endless; the possibilities for future innovations prove to be the same!
http://www.abc.net.au/science/photos/mathsinnature/