I first read the term 'Golden Spiral' about a year ago. At the time, I thought the words sounded so beautiful together that I delved a little deeper into the meaning behind them. Turns out the Golden Spiral (also called the Golden Mean or Golden Ratio) is a concept used in the arts but has its roots in mathematics.
'Some of the greatest mathematical minds of all ages from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.' —Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number
So what does that all mean? Well, it has been said that the Golden Spiral, although an actual mathematical equation, manifests itself over and over again nature.
'The spiral is derived via the Golden Rectangle, a unique rectangle which has the golden ratio (1:1.618). When a square section is removed, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle. Square removal can continue indefinitely with the same result. No other rectangle has this trait.
When you connect a curve through the corners of these concentric rectangles, you have formed the Golden Spiral. The Phythagoreans loved this shape for they found it everywhere in nature: the Nautilus Shell, Ram's horns, milk in coffee, the face of a Sunflower, your fingerprints, our DNA, and the shape of the Milky Way.' (pithemovie.com)
Here is a diagram of the Golden Spiral - you can see the original large rectangle and how, as each rectangle is defined, the curve is formed:
The human eye is naturally drawn through the curve of the Golden Spiral and it is in fact a concept used often by advertisers. Images and words are laid out to attract your eyes to the main product, which will most often lie where you would find the tight spiral of the curve. Check out http://munty13.blogspot.com/ for a great photo collage of examples of the Golden Spiral including the sky in Vincent Van Gogh's painting 'Starry Night', a curled up fern leaf, The Milky Way and a snail shell.
Once you know about the Golden Spiral, you will start to see it everywhere. My goal has become to find it in the viewfinder of my camera before I press the shutter.