Phi: The Golden Mean
The ancient Greeks, in investigating nature and extra-polating their findings to the study of art and architecture, developed the concept of the Golden Mean. The Greeks used this concept to name the pleasing proportion they find throughout nature of 1 to 1.6, expressed mathematically in the irrational number, 1.618033989. This concept is known by many names, including the Golden Selection, the Golden Proportion, the Golden Ratio, the Perfect Division, Phi, or simply the Greek letter Ø. I will use the terms “Phi” and “Golden Mean.”
More than two thousand years later, science continues to follow the Greeks’ lead. Nature’s use of the Golden Mean can be found in the animal, vegetable, and mineral kingdoms. Nothing appears to be so small or insignificant that it does not merit a pleasing proportion. Note, for example, the endlessly embellished hexagons of the snowflake or the perfect cubes found in mineral crystals. Human beings, a remarkably symmetrical creation themselves, appear to react instinctively and positively to forms that follow rigid geometric rules, whether in nature or art.
Today, we can see that even the DNA molecule, life’s single most important biological structure, is in the Phi proportion. One complete revolution of the DNA double helix measures 34 angstrom. The width of the DNA helix is 21 angstrom. The ratio 34 to 21 is 1 to 1.6.
The natural form that must fully expresses the Golden Mean is nature’s crowning achievement: the human body. The body begins its existence in the spiral pattern of an embryo. And when it matures, it exhibits Phi proportions in the primary relationships of its parts. The belly button divides the body, the brow divides the head, and the wrist divides the hand and forearm – all almost perfectly in the Phi proportion. Moreover, finger bones are in Phi proportion to each other, making a Golden Spiral when a fist is made, not everyone’s body exhibits perfect Phi proportions, but Phi will usually be seen as governing many of the body’s key relationships.
Other examples of Golden Spiral may be found in the profile of a wave, the vortex of a tidal whirlpool and our own solar system where the distance between the planets reflect Phi. Even the spiral of the beautiful natural nautilus shell (which is the logo of my Studio) follows the Golden Spiral.
Edward S. Philips, D.D.S.