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Phi (ø) The Devine Proportion Aka: the Golden mean the Golden section the Devine section
Value: 1.618… The Golden Section And Phi • the ratio of the whole line (A) to the large segment (B) is the same as the ratio of the large segment (B) to the small segment (C). A C B • In other words, AC is to CB, as CB is to AB. • This occurs only where A is 1.618... times B and B is 1.618... times C.
Phi and the Fibonacci Series • Leonardo Fibonacci discovered the series which converges on phi • In the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi. • Starting with 0 and 1, each new number in the series is simply the sum of the two before it. • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . • The ratio of each successive pair of numbers in the series approximates phi (1.618. . .) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.
Who ‘invented’/’discovered’ PHI • it might have been the ancient Greeks who built the famous Parthenon temple • It has also been suggested that the Egyptians who built the pyramids used it • the ancient Mexicans built the Sun Pyramid at Teotihuacan • Greek mathematician Euklides first one who has written down the real formula
The ‘Beautiful’ number • phi is a special number or ratio with tons of interesting properties. • It is seen in all of nature from microscopic crystals to spiral galaxies. • It even seems to be hard-wired into our brains as an archetype of beauty.
Phi and the Golden triangle • Ratio of one side to other is Phi • Can be seen in architecture (ancient to today) • Size of credit card • Noah's Ark uses a Golden Rectangle • The Ark of the Covenant is a Golden Rectangle
Phi and your body • Hand: Each section of your index finger, from the tip to the base of the wrist, is larger than the preceding one by about the ratio of 1.618 • The ratio of your forearm to hand is Phi • A peaceful heartbeat is said to beat in a Phi rhythm
Phi and Music • phi relationships are often found in the timing of musical compositions. As an example, the climax of songs is often found at roughly the phi point (61.8%) of the song, as opposed to the middle or end of the song. In a 32 bar song, this would occur in the 20th bar. • Phi proportion is in the design of violins high quality speaker wire.
Phi and Art • Use Phi when Painting faces (face proportion for beauty – eyes/nose/chin ) • Da Vinci used Phi – faces • DaVinci and Salvador Dali used Phi proportions in paintings of ‘The last supper’ • Georges Pierre Seurat (French Impressionist) divided canvas proportions using Phi
Phi proportions also exist in: • Architecture • Geometry • Population growth • Spirals (snail shell, sunflower seeds, petals) • Energy • Crystals • Solar system • Stock markets • Theology
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