Love this concept of the Fibonacci spiral= each square drawn is the sum of the last two squares drawn! Beautiful proportion lesson from The Helpful Art Teacher: THE SPIRAL
PHI: The Golden Ratio or Golden Section - a unique Ratio (or relationship between parts) that seems to be preferred by Nature as the best geometry for growth, energy conservation, elegance and has some fundamental relationships to the platonic solids and the Mandelbrot set. It was formally discovered by the Greeks and incorporated into their art and architecture, but it has been shown to occur even in prehistoric art, possibly as a function of Man's natural affinity for it's beauty.
The Golden Section 11 x 14 Art Print Mathematics by GeographicsArt
Another example of the spiral. This time its with a Nautilus shell. It's a perfect example of the golden ratio in nature as you can see by how both the shell and spiral expand by something like 1.5 its size every turn.