This spiral is based on a series of numbers called The Golden ratio or the Golden Mean. The Golden Mean is a ratio, one which has fascinated people for thousands of years, and can be seen in the art work of many cultures.
The "golden spiral" occurs frequently in nature. If you look closely enough, you might find a golden spiral in the head of a daisy, in a pinecone, in sunflowers, or in a chambered nautilus shell from the seashore.
The spiral is created from the golden rectangle, a unique rectangle which has the what is called "the golden ratio". Each rectangle in the spiral of rectangles has the same proportions, and it leaves a smaller rectangle behind which has the same golden ratio as the previous rectangle. The squaring 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. Students of the Greek mathematician Pythagorus 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.
The drawings below shows a Golden Spiral, and the steps used to construct this spiral. You can see more images and information at the following web page: http://mathforum.org/~sanders/geometry/GP21MoreCurves.html
The Golden Spiral can be constructed and then turned into a lovely hand-made card to give to a friend or family member as a birthday card, Valentine's Day card, or just to tell them how much you love them. The outside of the card, when colors or images are placed within the sections, might look like the one below, which includes images of sprirals found in nature. The images used here are (in order of smallest to largest) a yellow flower, a red flower, a green fern, a pink flower, a fractal image, a seashell, and a Chambered Nautilus shell.
