The document discusses the Golden Ratio and its applications. It begins by defining the Golden Ratio mathematically and describing the Fibonacci sequence. It then explains how the Golden Ratio appears in nature and has been used by artists, architects, and designers to achieve aesthetic proportions. Examples mentioned include the proportions of the human body, seashells, and plant structures, as well as applications in photography through the Rule of Thirds composition technique.

1. THE GOLDEN
RATIO…
AN ENGINEER’S PERSPECTIVE…

2. WHAT IS IT?
1+ 5
j=
2
2

3. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
3

4. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
4

5. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
5

6. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
6

7. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
7

8. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181,
6765…
8

9. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
9

10. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
10

11. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
11

12. FIBONACCI…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65…
12

13. GOLDEN RATIO…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65… 1
13

14. GOLDEN RATIO…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
65… 2
14

15. GOLDEN RATIO…
1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, 233, 377, 610,
987, 1597, 2584, 4181, 67
3
65… = 1.5
2
15

16. GOLDEN RATIO…
3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946
1,2, , , , , , , , , , , , , , , , , ,
2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
1+ 5
j=
2
j = 1.61803...
16

17. WHY IS IT USEFUL?
17

18. PHOTOGRAPHY…
18

19. RULE OF THIRDS?
19

20. RULE OF THIRDS?
20

21. RULE OF THIRDS?
21

22. RULE OF THIRDS?
22

23. RULE OF THIRDS?
23

24. RULE OF THIRDS?
24

25. RULE OF THIRDS?
25

26. RULE OF THIRDS?
26

27. NEAR ENOUGH?..
27

28. SO WHAT!
28

29. Courtesy of Flickr - Kyri Sarantakos
Licensed under
GREEKS…
29

30. Courtesy of Flickr - Kyri Sarantakos
Licensed under
PROPORTIONS…
1.0
1.61803
30

31. PLATONIC SOLIDS…
Dodecahedron
Octahedron
Icosahedron
Cube
31
Tetrahedron

32. BUCKY FULLER…
Courtesy of Flickr - caribb
Licensed under
32

33. NATURE…
Courtesy of Flickr - eEditor
Licensed under
33

34. NATURE…
34

35. BIOMIMETICS…
Courtesy of Flickr - kibuyu
Licensed under
35

36. THANK YOU…
36