1.61803398874989484820458683436563811772030917980
5762862135448622705260462818902449707207204189391
1374847540880753868917521266338622235369317931800
6076672635443338908659593958290563832266131992829
0267880675208766892501711696207032221043216269548
6262963136144381497587012203408058879544547492461
8569536486444924104432077134494704956584678850987
4339442212544877066478091588460749988712400765217
0575179788341662562494075890697040002812104276217
7111777805315317141011704666599146697987317613560
0670874807101317952368942752194843530567830022878
5699782977834784587822891109762500302696156170025
0464338243776486102838312683303724292675263116533
9247316711121158818638513316203840052221657912866
7529465490681131715993432359734949850904094762132
2298101726107059611645629909816290555208524790352
4060201727997471753427775927786256194320827505131
2181562855122248093947123414517022373580577278616
0086883829523045926478780178899219902707769038953
2196819861514378031499741106926088674296226757560
523172777520353613936...
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
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
The Formulae
n
fn = Φ / 5½
Or
n
fn = Φ / (Φ + 2)
Φ In Mathematics
Arithmetic mean : c = ( a + b ) / 2
Geometric Mean : c = ( a x b ) / 2
The Golden Mean
a:b=b:c
and a = b + c
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…
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
n
+ 1 / Φ = a whole number
For any odd integer n:
Φ
n
n
- 1 / Φ = 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
Salvador Dali’s "The
Sacrament of the Last
Supper"
Da Vinci's "The Last
Supper"
Φ In Art & Architecture
Φ in Architecture
Φ in Pyramid
Φ in Notre Dame - Paris
Φ in Greek Architecture
Φ In Art & Architecture
Φ in Architecture
United Nations building
CN Towers - Toronto
Φ In Art & Architecture
Φ in Colors
PhiBar By Michael Semprevivo
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
One one two, three five eight
Φ In Art & Architecture
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
0
A
1
1
A
1
2
A
B
3
A
B
C
4
A
B
C
D
5
A
B
C
D
E
6
A
B
C
D
E
etc.
1
2
2
3
3
4
B1
5
F
6
5
B1
B2
C1
B1
B2
B3
7
8
9
C1
10
8
C2
11
D1
12
B11
13
13
etc.
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