The Golden Ratio

1
The Golden Ratio
What is it? 1.618033988749895... Also
known as Phi (rhymes with fly) it is an
irrational number like pi ( 3.14159265358979...
), but one with many unusual mathematical
properties.
2
1.618033988749895
The Golden Ratio
This ratio (Phi) was known to the Greeks as
the "dividing a line in the extreme and mean
ratio. It was known to Renaissance artists as
the "Divine Proportion. It is also called the
Golden Section, Golden Ratio and the Golden Mean.
3
1.618033988749895
The Golden Ratio
Phi, like Pi, is a ratio defined by a geometric
construction Just as pi (p) is the ratio of the
circumference of a circle to its diameter, phi
is the ratio of the line segments that result
when a line is divided in one very special and
unique way.
4
1.618033988749895
The Golden Ratio
The ratio of the length of the entire line (A) to
the length of larger line segment (B) is the same
as the ratio of the length of the larger line
segment (B) to the length of the smaller line
segment (C).
5
1.618033988749895
The Golden Ratio
This happens only at the point where A is 1.618
... times B and B is 1.618 ... times C.
6
1.618033988749895
The Golden Ratio
You can also use this golden ratio to form a
golden rectangle
This rectangle is unique because the resulting
rectangle On the right is similar to the
original rectangle After drawing a square within
the rectangle. This can be done again, and again
and again.
7
1.618033988749895
The Golden Ratio
Until the pieces become too small to see. The
spiral Drawn within the squares is known as the
golden spiral
8
1.618033988749895
The Golden Ratio
The reciprocal of Phi is known as phi (with a
lower case p.)
This reciprocal relationship is unique in
mathematics. The reciprocal of Phi (1.
6180339887 ) is 0.6180339887. Which is Phi
minus 1.
9
1.618033988749895
The Golden Ratio
What makes phi even more unusual is that it can
be derived in many ways and shows up in
relationships throughout the universe.
10
1.618033988749895
The Golden Ratio
Mathematically Leonardo Fibonacci discovered the
series which converges on Phi a simple
numerical series that is the foundation for a
mathematical relationship with 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.
11
1.618033988749895
The Golden Ratio
In Geometry, Phi can be found in the following
figures Inscribed within a circle.
12
1.618033988749895
The Golden Ratio
In the human body
13
1.618033988749895
The Golden Ratio
In the human body
14
1.618033988749895
The Golden Ratio
In Nature
15
1.618033988749895
The Golden Ratio
In Nature
3 Lilies 5 Buttercups, Roses 8 Delphinium 13
Marigolds 21 Black-eyed susans 34
Pyrethrum 55/89 Daisies
16
1.618033988749895
The Golden Ratio
In Nature
17
1.618033988749895
The Golden Ratio
In Nature
DNA has spirals in phi proportions DNA in the
cell appears as a double-stranded helix referred
to as B-DNA. This form of DNA has a two groove in
its spirals, with a ratio of Phi in the
proportion of the major groove to the minor
groove, or roughly 21 angstroms to 13 angstroms.
18
1.618033988749895
The Golden Ratio
In the solar system
SATURN
19
1.618033988749895
The Golden Ratio
THE UNIVERSE
Studies have revealed that the math adds up if
the universe is finite and shaped like a
dodecahedron,
The faces of which Are pentagons that Exhibit Phi.
20
1.618033988749895
The Golden Ratio
In Architecture
21
1.618033988749895
The Golden Ratio
In Architecture
22
1.618033988749895
The Golden Ratio
In Architecture
23
1.618033988749895
The Golden Ratio
In Art
24
1.618033988749895
The Golden Ratio
In music
There are 13 notes in the span of any note
through its octave. A scale is comprised of 8
notes, of which the 5th and 3rd notes create the
basic foundation of all chords, and are based
on whole tone which is 2 steps from the root
tone, that is the 1st note of the scale.
25
1.618033988749895
The Golden Ratio
In music
26
1.618033988749895
The Golden Ratio
In Everyday items
A perfect golden rectangle
27
1.618033988749895
The Golden Ratio
In Everyday items
Blood pressure recommendations 130/80 which
is 1.625 which is freakishly close to
1.618033988749895
28
1.618033988749895
The Golden Ratio
Is all this a coincidence? How could this all
be explained? Math.Go figure!
29
1.618033988749895
The Golden Ratio
SMILE!