"Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

-- Johannes Kepler [1571-1630]

Also known as The Goden Section, Golden Ratio, and The Divine Proportion.

In nature, there is a fundamental ratio which is found in countless places. This ratio of 1.618:1 is called Phi, and since it's a part of the world around us, it evokes emotion and asthetic feelings. Examples of Phi in nature are the spirals in sunflowers which expand in a Phi proportion, as do pine cones and pineapples. In daisys, the florets grow in two spirals, one being 21 and the other being 34. Phi. The chambered nautilus - nature's perfect scroll - grows in a ratio according to the Golden Mean.

In humans, the average ratio of the mouth to nose is Phi. Measure your total height and then measure your height just to your navel. Divide the total height by your "navel" heights. The result is be a number close to the Golden Mean. In the lub-to-dub of the human heartbeat, the dub is 1.618 times longer than the lub.

The proportions of pyramids in Giza are extremely close to Phi, and Renaissance masters used the Phi ratio in everything from sculpture to canvas size. Today, the Golden Mean is the preferred ratio for many things, including windows and table tops. Stradavari used the Golden Mean to determine fingerboard size and placement of f-holes in his violins. Tthere are countless examples of Phi in music, where the mood, a bridge, or key changes at a Phi location.

FIBONACCI SERIES:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on to infinity...

Fibonacci, an Italian painter who while studying the way plants grew, realized many followed the above sequence. After a plant grew one flower, it would grow one more, then two more, and so on, following the pattern exactly. After the number 13, the numbers increase according to Phi. The Fibonacci Series has an interesting relationship to the chambered nautilus mentioned above.

THE GOLDEN RECTANGLE can be further divided into smaller golden rectangles and arcs of circles added to make a scroll. In every part of the world and in every culture, the scroll has been used to decorate everything from carpet to cathedrals. We humans like scrollwork, as proven by the vast amout used in design from time immemorial. Since the scroll is formed on the Phi proportions, could it be that we're simply genetically hard-coded to like it? It's interesting to think about.

As you look around, you'll begin to see the Golden Mean everywhere, from buildings to paintings, and in nature. I think that an awareness of Phi is certainly valuable information, but I don't take measurements and do layouts that adhere to a 1.618:1 ratio (but it would certainly be ok to do so). I think that in many instances a Phi ratio happens unconciously during design, as it looks asthetically pleasing.

There is much written information on the Golden Mean. If you are interested in the subject (and I hope you are), an internet search will provide a lot of very interesting reading.