Golden ratio

GOLDEN RATIO
Dr. R. KALAIVANAN

THE GOLDEN RATIO
 Two quantities are in the GOLDEN RATIO if the ratio
of the sum of the quantities to the larger quantity is
equal to the ratio of the large quantity to the smaller
one.

•Human anatomy
•Music
•Architecture
•Photography
•Solar system
•Logo

GOLDEN RATIO IN DNA
DNA consists of two spirals and molecules. Between
two spirals’ lengths there are 34 angstroms, and its
width is 21 angstroms(21 and 34 in Fibonacci series),so
it has golden ratio.

IN THE ASPECT RATIO OF DNA
SPIRAL
It measures 34angstroms long by 21 angstroms wide-
for each full cycle of its double helix spiral. 34 and 21
,of course, are numbers in the Fibonacci series and
their ratio, 1.6190476 closely approximates phi,
1.6180339

GOLDEN RATIO IN HEART RHYTHM
 Man’s heart is beaten uniformly.
 The ratio of maximum(systolic) pressure to the
minimum (diastolic) pressure is equal , on the average
to 1.6 that is close to the golden proportion.

GOLDEN RATIO IN MUSIC
 The black &white keys
represent the ratios of musical
proportion.
 There are 8 white keys and 5
black keys,
 8:5=1.6-5:8=0.625
 The black keys are in groups
of 2 and 3. the series 2:3:5:8 is
part of the fibonacci series. All
these ratio close to ф,which is
1.618

GOLDEN VIOLIN
•Musical
instrument design
is often based on
phi, the golden
ratio.
• Fibonacci and
phi are used in the
design of violins.
• even in the
design of high
quality speaker
wire.

GOLDEN RATIO IN ARCHITECTURE
 The length of the base of the
pyramid is approximately
1+1=2
 The height of an isosceles
traingular face is
approximately phi(ф).
 The height of the pyramid is
approximately the square root
of phi.(√ф)
 The height can then be found as
√ф- 4/п

GOLDEN RATIO IN TAJ MAHAL
 The main building of the Taj Mahal was designed
using the golden ratio.
 This is why it looks so perfect
 The rectangles that served as the basic outline for the
exterior of the building were all in the golden
proportion.

GOLDEN RATIO IN PHOTOGRAPHY
 There’s one other way to use
the golden ratio to compose a
photograph
 Instead of using the spiral,
create a grid like in the rule of
thirds,but one that uses a
1:1.618 ratio, instead of
dividing the frame into equal
parts.

GOLDEN RATIO IN HUMAN FACE
With Golden Ratio Without Golden Ratio

GOLDEN RATIO IN SOLAR SYSTEM
•The diameter of saturn is
very close to a phi relatioship,
with the diameter of its rings
as illustrated by the green
lines.
•The inner ring division is in
a relationship that is very
close to phi with the
diameter of the rings outside
the sphere of the planet
illustrated by the blue lines.

GOLDEN RATIO BETWEEN SUN, VENUS, EARTH
 Venus orbits the sun in 224.695 days
while earth orbits the sun in 365.242
days, creating a ratio of 813(both
fibonacci numbers) or 0.615(roughly
phi). thus conjuctions of Earth and
Venus occur every 8 orbits of the earth
around the sun and every 13 orbits of
Venus.
 Mercury, on the other hand,orbits the
sun in 87.968 earth days,creating a
conjuction with earth every 115.88
days. thus there are 365.24/115.88
conjuction in a year or 22 conjuctios
in 7 years, which is very close to phi

Golden ratio

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Golden ratio