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Φ The Omnipresent

A Tour of the PHI-NEST Phi–nomenon : A Brief Introduction Take a Look Around :Phi is Everywhere by Bivas Das Can’t Live Without :Phi in Mathematics by Ishan Chakraborty About Human Creativity :Phi in Art and Architecture by Sourish Sengupta Time to Know Ourselves :Phi in Life by Amritam Sarcar Conclusion : The Omnipresent

Φ Is Everywhere Φ in Energy Φ in Solar System Φ In Universe

Φ In Energy Unusual signals at Phi Hertz are being received on Earth  

Φ In Solar System Saturn's rings are divided at two phi points                                                                                                                                       The Cassini division in the rings of Saturn falls at the Golden Section of the width of the ring.

Φ In Solar System Venus and Earth reveal a phi relationship The shape of the Universe itself is a dodecahedron based on Phi

Φ In Universe New findings in 2003 reveal that the shape of the Universe is a Dodecahedron based on Phi The connection to Phi is found in the Pentagons that form the faces of the Dodecahedron

In the rabbit hole…

Φ In Mathematics Derivation of Φ Fibonacci Series The Golden Mean The Numbers 5, 89 and 109 Phi’s Additive relationship Relations between Powers of Φ Φ in Geometry

Φ In Mathematics The Derivation of Φ Φ2 - Φ1 – Φ0 = 0 or Φ2 = Φ + 1

Φ In Mathematics Fibonacci Series & Φ Or The Formulae fn = Φ n / 5½ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . The Formulae fn =  Φ n / 5½ Or fn =  Φ n / (Φ + 2)

Φ In Mathematics The Golden Mean Arithmetic mean : c = ( a + b ) / 2 Geometric Mean : c = ( a x b ) / 2 The Golden Mean a : b = b : c and a = b + c

Behavior of few Numbers Φ In Mathematics Behavior of few Numbers Φ = 5 (.5) * .5 + .5 Φ = e asinh(.5) fn =  Φ n / 5½ 1/89 = .011235 95505617977528089887640449438202247191… 1/109 = .009174311926605504587155963302752293577981651376146788 9908256880733944954128440366972477064220183486238532110…

Phi’s Additive Relationship Φ In Mathematics Phi’s Additive Relationship Φ n+2 = Φ n+1 + Φ n Powers of Φ For any even integer n: Φ n + 1 / Φ n = a whole number For any odd integer n: Φ n - 1 / Φ n = a whole number

Φ In Mathematics Phi in Geometry Circum-circle Square in a Semi Circle Pentagon in a Circle

Φ In Mathematics Phi In Bulky Balls

Φ In Mathematics Spiral and Phi 12 + 12 + . . . + f(n)2 = f(n) * f(n+1)  

Φ In Art & Architecture Φ in Art Φ in Architecture Φ in Colors Φ in Music Φ in Poetry

Φ In Art & Architecture Phi In Art Φ = B/A or B/(B+C)

Φ In Art & Architecture Phi In Art Da Vinci's "The Last Supper" Salvador Dali’s "The Sacrament of the Last Supper"

Φ in Greek Architecture Φ In Art & Architecture Φ in Architecture Φ in Pyramid Φ in Notre Dame - Paris Φ in Greek Architecture

United Nations building Φ In Art & Architecture Φ in Architecture United Nations building CN Towers - Toronto

PhiBar By Michael Semprevivo Φ In Art & Architecture Φ in Colors PhiBar By Michael Semprevivo

Φ in Musical instruments Φ In Art & Architecture Φ in Music Φ in Musical instruments

Φ In Art & Architecture Φ in Music Fibonacci Ratio Calculated Frequency Tempered Frequency Note in Scale Musical Relationship 1/1 440 440.00 A Root 2/3 293.33 293.66 D Fourth 3/5 264 261.63 C Minor Third 5/8 275 277.18 C# Third

Φ In Art & Architecture One one two, three five eight Sounds so simple, nothing great Thirteen, twenty-one, thirty-four The hinges creak on an opening door A repeating patter of the masters hand Signing his work, the universal plan Learn to look, the pattern's plain to see In the smile you flash, the dance of the honeybee In the spirals of the pine cone and little acorn cap In spiral arm galaxies and the ocean's wave whitecap In the swirl of the seashell, the air vortex of a wing The hurricane's eye and a thousand unseen things Welcome to the mystery of the Greek letter phi The measurement of beauty to the human eye The golden ratio, one point six one eight One, One, Two; Three, Five Eight -Benjamin Moon 1.618 ad infinitum! Never repeating, always intriguing Fibonacci born; phi! Golden Section behold! Creation sequence, nature's frequence Mathematical phenomena; phi! Heaven's divine proportion! Ancient mystery, living history Infinite and eternal; phi! -John Sarber

Φ In Life Φ in Human Hand Φ in Human Face Φ in Human Teeth Φ In Human Body Φ In Human Beauty Φ In Human Heart Beat Φ in Animals Φ in Plants Φ in Population and Growth

Φ In Human Hand Your finger shows Fibonacci Series The ratio of your forearm to hand is Phi

Φ In Human Face Phi defines the dimensions of the human profile The human face is based entirely on Phi Human head is based on Phi

Φ In Human Teeth Phi is found in the dimensions of the teeth, mouth, lips and even your smile. Dr. Levin’s Phi Dental Grid Software Golden Mean Gauge

Φ In Human Body The Divine Proportion in the Body The human body is based on Phi and 5 5 appendages on each of the fingers and toes 5 openings on the face. 5 senses in sight, sound, touch, taste and smell.

Φ In Human Beauty Asian 1350 B.C. Egypt Black 500 B.C. Greece Marquardt Beauty Analysis Caucasian 164 A.D. Rome                                                                                                           

Φ In Human Heart Beat A peaceful heartbeat is said by some to beat in a Phi rhythm … EKG's show a resemblance to the Fibonacci Convergence

Φ In Animals Divine Proportion in nature

Φ In Animals Examples of the Divine Proportion and Golden Section can be found in fish, birds, mammal and insects.

Φ In Plants Fibonacci numbers in plant spirals and branching Plants illustrate the Fibonacci series in arrangements of petals, leaves, sections and seeds. Plants such as pinecones, pineapples and sunflowers illustrate Fibonacci numbers. 

Φ In Population & Growth The Fibonacci series was discovered by studying population growth  How many pairs will there be in one year? Pair A of rabbits gives birth to pairs B, C, D and E.  Each of these in turn gives birth to pairs B1, B2, B3, C1, and C2, and this continues, etc.  Month Rabbits from A: from B: from C: D: B1: Total A   1 2 B 3 C 4 D B1 5 E B2 C1 8 6 F B3 C2 D1 B11 13 etc. 7 9 10 11 12

Φ is Omnipresent Conclusion "All science is physiology.  All physiology is chemistry.  All chemistry is physics.  All physics is math. All math is life. All life is phi. " - Dr. Stephen Marquardt Φ is Omnipresent