1. Subject Teacher:- Mr. Ch. Narendra Kumar

2. Before seeing this
PPT, first watch the
video for better
understanding
about The Golden
Ratio.

3. 
Well, before we answer that
question let's examine an
interesting sequence (or list) of
numbers.
Actually the series starts with 0, 1
but to make it easier we’ll just start
with 1,1
What is the Golden Ratio?

4. To get the next number we
add the previous two
numbers together.
So now our sequence
becomes 1, 1, 2

5. Here is what our sequence should
look like if we continue on in this
fashion for a while:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
377, 610…

6. Leonardo Fibonacci
Really Famous
&
Really Smart

7. Now, I know what you might
be thinking:
"What does this have to do
with the
Golden Ratio
?????????

8. Let's look at some of the ratios of
these numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377, 610…

9. Next number
divided by
previous
number gives us
Golden ratio
When we proceed
next then this
number converges
to 1.68
2/1 = 2.0
3/2 = 1.5
5/3 = 1.67
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615
34/21 = 1.619
55/34 = 1.618
89/55 = 1.618

10. The Golden Ratio is what we
call an irrational number: it has
an infinite number of decimal
places and it never repeats itself!
Generally, we round the Golden
Ratio to 1.618.

11. Lets Check

12. Spirals of a pinecone

13. Where spirals from the center have 5
and 8 arms, respectively (or of 8 and
13, depending on the size)- again, two
Fibonacci numbers
(Gives golden ratio)

14. Golden Ratio in Sun Flower

15. If you look at a sunflower, you will
see a beautiful pattern of two
spirals, one running clockwise and
the other counterclockwise.

16. If we count the
spirals we will find
that there are 21 or
34 running
clockwise and 34
or 55 running
counterclockwise,
respectively-all
Fibonacci numbers

17. Some plants express the Fibonacci
sequence in their growth points,
the places where tree branches
form or split.
One trunk grows until it produces
a branch, resulting in two growth
points & then three , five so on…

18. These Fibonacci
numbers gives
“Golden Ratio”

19. DNA molecules follow this
sequence, measuring 34
angstroms long and 21 angstroms
wide for each full cycle of the
double helix

20. The Ahmes papyrus of Egypt
gives an account of the
building of the Great
Pyramid of Giaz in 4700 B.C.

21. It is simply constructed on
Golden Ratio

22. It was used it in the design of Notre
Dame in Paris, which was built in the
1163 and 1250.

23. In India, it was used in the construction
of the Taj Mahal, which was completed in
1648.

24. In the United Nations building, the
width of the building compared
with the height of every ten floors
is a “Golden Ratio”

25. Does Beauty exist in Golden
Ratio

26. You can check Yourself

27. You need some calculations

28. The Perfect Face -
Golden Ratio Beauty
Calculator

29. Now tell
Which smile is more
appealing?

31. Because its length to width ratio
gives
“Golden number”

32. Look at the following
rectangles
Now ask yourself, which of them seems
to be the most naturally attractive
rectangle?

33. If you said the first one, then you
are probably the type of person
who likes everything to be
symmetrical.
Most people tend to think that the
third rectangle is the most appealing

34. Have you figured out why the third
rectangle is the most appealing?
That's right - because the ratio of its
length to its width is the
Golden Ratio!
For centuries, designers of art and
architecture have recognized the
significance of the Golden Ratio in
their work.

36. Now let's go back and try to
discover the Golden Ratio in art.We
will concentrate on the works of
Leonardo daVinci, as he was not
only a great artist but also a genius
when it came to mathematics and
invention.

38. Even in Mona Lisa Painting
“Golden ratio exist”

39. Take A Good Look At
Yourself In The Mirror

40. Human body is made on
“Golden Ratio”

41. You will notice that most of your
body parts follow the numbers
1,2,3&5
You have one nose, two eyes, three
segments to each limb and five
fingers on each hand

42. The proportion of upper arm to hand +
forearm is in the same ratio of 1: 1.618

43. You can also apply the Golden Ratio to
other element’s width in relation to its
height or vice-versa.
This produces aesthetically pleasing
elements with the Golden Ratio
proportions.

44. This Car is looking nice…………..
Ofcource its Shape is made on the concept Of
Golden Ratio

45. ANY QUESTIONS?

46. Thank you one
and all....
BY:- Nivesh Krishna
Class:- X-D