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# Phi ( ø ) The Devine Proportion

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).

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## Phi ( ø ) The Devine Proportion

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1. Phi (ø) The Devine Proportion Aka: the Golden mean the Golden section the Devine section

2. 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.

3. 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.

4. 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

5. 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.

6. 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

7. 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

8. 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.

9. 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

10. Phi proportions also exist in: • Architecture • Geometry • Population growth • Spirals (snail shell, sunflower seeds, petals) • Energy • Crystals • Solar system • Stock markets • Theology