Phi (letter)

Phi (upper case Φ, lower case φ or {{phisymbol}}) is the 21st letter of the Greek alphabet. It is pronounced fee by modern Greeks, or fie (depending on context and, often, personal inclination). In the system of Greek numerals it has a value of 500.

Phi in History and Nature

Phi (Φ = 1.6180339887...) is an irrational number like π (π = 3.141592653...). Φ and π are both ratios defined by particular Euclidean geometries, with Φ being the division of a line ?so that the ratio of the lesser part to the greater part is the same as the ratio of the greater part to the whole.1? Φ is often referred to as the Golden Section, the Divine Proportion, the Golden Ratio and the Golden Mean.

Related Topics:
Golden Section - Divine Proportion - Golden Ratio - Golden Mean

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This ratio Φ can be found in many natural constructs such as in human and animal proportions (i.e. the arrangement of physical features). Φ relationships can be found in DNA, among the planets of the Solar System (as in Kepler's Laws), and so on.

Related Topics:
DNA - Kepler's Laws

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Many argue that Φ is also used by humans in such things as art, architecture and music for the balance it produces in designs. However, there are some caveats to this. For example, some claim one can find Φ in the structure or design of the pyramids. Is Φ intentional in the pyramids or merely the result of what is good geometrical design? It is probably the latter. Architecture is often designed with balance and stability which necessitates geometries that contain Φ, though these geometries are not always necessary. Φ may be intentional in some structures, but it is accidental or inadvertent in others.

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Fibonacci Series

This is the Fibonacci series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. . .etc. It is very simply explained as each number in the series being the sum of the previous two numbers. The ratio of each successive pair of numbers (starting with 3/2) in the series approximates Φ (i.e. 8 divided by 5 is 1.6). The accuracy of these ratios? approximations to Φ increases considerably as you go through the series. Φ can also be used to estimate any number in the Fibonacci series: fn = Φn / 5½.

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Thise Fibonacci series is the basis of the spiral patterns common in nature: In shells, hurricanes, whirlpools, spiral galaxies, DNA and plant life. Φ is all around us. For example: The ratio of scales in the opposing spirals around a pine cone are 5:8; bumps on a pineapple are 8:13; seeds in a sunflower are 21:34. All of these ratios are adjacent pairs in the Fibonacci series.

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Biblical Indications of Phi

Exodus 25:10 writes: ?Have them make a chest of acacia wood ? two and a half cubits long, a cubit and a half wide, and a cubit and a half high.? Here we find that ?The ratio of 2.5 to 1.5 is 1.666..., which is as close to phi (1.618...) as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Golden Section, or Divine Proportion. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.2? Genesis 6:15 writes ?This is how you are to build it: The ark is to be 450 feet long, 75 feet wide and 45 feet high.? Hence, 75 by 45 feet is also in the ratio of 5 to 3, or 1.666..., another ?close approximation of phi not visibly different to the naked eye. Noah's ark was built in the same proportion as ten arks of the covenant placed side by side.3?

Related Topics:
Exodus - Ark of the Covenant - Genesis - Noah's ark

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These indications of Φ may or may not have been intentional. However, as with the other examples of Φ in manmade creations, they are evidence of a trend for man to use the same logic imbedded in the universe.

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