The document discusses the prevalence and applications of the golden ratio, also known as phi, in mathematics, nature, art, architecture, music, and the human body. Some key points include: - The golden ratio is approximately 1.618 and can be seen in the proportions of flowers, shells, galaxies, DNA, and the human face/body. - It has been used intentionally in architecture for centuries, appearing in structures like the Parthenon and pyramids of Giza. - The Fibonacci sequence is related to the golden ratio and can be observed in patterns in nature as well as the piano keyboard. - Artists, architects and designers continue to find inspiration from the golden ratio's

1. The Application Mathematics
- The golden ratio-
1.618…

2. !ncredible math
01 All of us can remember the
calculation after hearing the
word math
Calculation
Cycle of Math
All the above cycle of this math is progressively developed from the age of hunting to before the industrial revaluation this
02 Calculation let a way to analysis
The analysis of human
transform the math to its
application
Analysis
04 All the above process inspire
the human to calculate ,analysis
and apply them
Inspiration
03 The human brain always things
for infinity which change
analysis to application
Application
All the above process inspire
the human to calculate ,analysis
and apply them
Inspiration

3. !cycle of maths
01
Calculation
Cycle of Math
Yes after the industrial revaluation there is change in their cycle the inspiration change to corporation
02
Analysis
04
Inspiration
03
Application
Yes the term inspiration changes
to capital which becomes a
platform to earn
Corporation

4. THE INCREASE IN THE INDUSTRIALIZATION
ALTHOUGH CHANGE THE INSPIRATION INTO
CORPORATION
This increase in industrialization increase
the demand for the efficient products to satisfy
the growing population all the effect of
industrialization forced the maths to give solution
for the growing issue on the field of economy
which results in producing a large amount of
revolution in the field of industry this forced
maths to apply their models into products to
satisfy the economy which became the
corporation
Effect of Industrialization

5. Choose any one from the below
A
C
B

6. A
B
C

7. A
C
B

8. A
C
B

9. B
A
C
A
Majority of our answer are

10. The reason behind them is same

11. ∆Why do certain shapes seem more appealing than
others?
∆Have you ever wondered how similar you are to your
favorite musician, actor, athlete, or other important
figure?
∆How can mathematics create beauty?
∆What is the common element in many of the things that
we find beautiful.

12. The answer for the above question is THE GOLDEN RATIO
YES ,The answer is maths
A "sacred ratio" used in the building of
the pyramids of Egypt 2,600 years ago
Fibonacci series is based on the ratio
Portrait Mode is also based on the ratio

13. THE GOLDEN RATIO
PHI
"A straight line is said to have been cut in extreme and mean ratio
when, as the whole line is to the greater segment, so is the
greater to the less." ~Euclid
What this means is that if you divide a line into two segments,
the ratio of the larger of the sections in relation to the entire
segment, is equal to the ration of the smaller section, to the
longer section. Or, if you were to look at the above line, and
create 2 segments within it according to the golden ratio, the
total length "a+b", is proportional to segment "a" in the same
way that "a" is proportional to the shorter segment, "b".
In other words...

14. The Golden Ratio: the math
the Golden Ratio is a special number approximately equal to
1.6180339887498948482
one way to visually understand it is with a line segment

15. What is the "Golden Ratio"?
According to mathematicians as far back as the ancient
Greeks and Egyptians, the element of perfection is a ratio.
The Greek mathematician Euclid defined the golden ratio
over two thousand years ago, in 300 BC, while working with
ratios present in geographic figures. It is a proportion used
to describe two things, mathematically similar.
The Golden Ratio is known by many other names, such as
the golden mean, the divine proportion, or the golden
proportion. It is represented by the Greek letter Phi (φ),
and is an irrational mathematical constant approximately
equal to 1.6180339887.

16. The Golden Ratio: the math
then a mathematical equation can be established through the ratio
b = a
a a + b
solving for a, we end up with
a = (1 + sqrt(5))
2
= phi 
= 1.618033988749
by cross-multiplying we get ab +
b2 = a2
or if we substitute 1 for b, then
a2 = a + 1

17. The Golden Ratio: Fibonacci sequence
Fibonacci sequence =
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
where 5/3 = 1.6666… and 8/5 = 1.6
and 13/8 = 1.625 and 21/13 = 1.615…
and 34/21 = 1.61904… and so on,
each more closely approximating the
Golden Ratio

18. APPLICATION ON PHI
It is naturally oriented with all living species, every
object in the world something based on the phi
ART
DESIGNING
ASTROLOGY
SPACE CALUCATION
ARCHITECH
PLASTIC SURGERY
………………….ETC
WE MAY DEFINE ANYTHING BASED ON THEM

19. Beauty in Art

20. The Golden Section in Music
• ~ Stradivari used the golden section to
place the f-holes in his famous violins
• ~ Baginsky used the golden section to
construct the contour and arch of violins
• ~ Beethoven used the golden section in his famous Fifth Symphony
• ~ Opening of the piece appears at the golden section point (0.618)
• ~ Also appears at the recapitulation, which is Phi of the way
through the piece
The Golden Section in Music Continued

21. How about in music?
Lets take a look at the piano keyboard…do you see
Anything familiar?
Count the number of keys (notes) in each of the brackets…
You will see the numbers 2,3,5,8,13….coincidence?
Does it look like the Fibonacci sequence…it should because it is!

23. Beauty in Nature

24. Have you ever noticed that most flowers contain a pattern?
The number of petals on a flower is often one of
the Fibonacci numbers: 3, 5, 8, 13, 21, 34 or 55?

27. The Golden Ratio is also a logarithmic spiral.
For every 90 degree turn, the radius of the
spiral grows by a factor of the phi.

28. In addition to natural patterns found here on
earth, the spiral pattern of the Golden Ratio
can also be seen in the pattern of our galaxy.

29. Beauty of the Human Body

30. The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by
21 angstroms wide for each full cycle of its double helix spiral.
DNA spiral as a Golden Section
B-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.

31. 1350 B.C. Egypt 500 B.C. Greece 164 A.D. Rome 1794 A.D.
Asian Caucasian Black
Beauty is in the eye of the beholder.
Does beauty vary by race, culture or era?

32. This two-dimensional visual of the human face is based
upon the Golden Ratio. This special number is believed
to symbolize perfect natural harmony.
This mask of the human
face is based on the
Golden Ratio. The
proportions of the length
of the nose, the position
of the eyes and the
length of the chin, all
conform to some aspect
of the Golden Ratio.

33. Look at your fingers closely. If you
measure the length of the longest
finger bone, and then the length of
the finger next to it, and then
divide the longer length by the
shorter one, you should get a
number close to 1.168.
All parts of the human body are
proportional to this number. In
fact, if your face is symmetric and
follows this ratio, you are often
said to be of exquisite beauty.

36. The ratio of your forearm to hand is Phi

37. Your hand shows Phi and the Fibonacci Series
your index finger.

38. The Human Body
The human body is based on Phi and 5
The human body illustrates the Golden Section. We'll use the same building blocks again:

39. Beauty in Architecture

40. The Parthenon
The exterior dimensions
of the Parthenon form a
Golden Ratio in many of
the proportions.
The Great Pyramid of Giza
Half of the base, the slant
height, and the height from
the vertex to the center
create a right triangle. When
that half of the base equal to
one, the slant height would
equal to the value of Phi and
the height would equal to the
square root of Phi.

41. The Golden Section in Architecture Continued
• ~ Golden section can be found in the design of Notre Dame in
Paris
• ~ Golden section continues to be used today in modern
architecture
United Nations Headquarters Secretariat building

43. The Golden Section on power
• ~ Is the ratio of the side of a regular pentagon to its
diagonal
• ~ The diagonals cut each other with the golden ratio
• ~ Pentagram describes a star which forms parts of
many flags
European Union
United States

44. The Golden Section on computer
Lot of company are working on the filed to develop the better
looking logo
Now the company are working on the camera based on the phi
only
A company which works with phi to exchange the power of phi

45. Even though I had given enough example on some fields, there is lot
of field which are working with the phi to create the future such
fields are plastic surgery, space
Plastic surgery they are working with burned case to recover the
reality they are working on them
Space mathematicians are working to find the way to create the
worm hole to transform the spaace technology to next level
The Golden Section on other

46. Gurus

47. Conclusion
The divine proportion has inspired thinkers of all
disciplines like no other in the history of mathematics.
And its mystery is yet to be unlocked. With its
presence everywhere the possibilities of applications
are endless