Golden Ratio, Fibonacci Numbers, and the Golden Spiral

Transcription

1 Golden Ratio, Fibonacci Numbers, and the Golden Spiral by University of Mobile

2 Creation Reveals God The heavens are telling of the glory of God; and their expanse is declaring the work of His hands. Day to day pours forth speech, and night to night reveals knowledge. There is no speech, nor are there words; Their voice is not heard. Their line has gone out through all the earth, and their utterances to the end of the world. Psalm 19:1-4a (NAS)

3 Golden Rectangle

4 Golden Rectangle

5 Golden Rectangle x {z x }

6 Golden Rectangle x {z x x 1 = 1 x 1 }

7 Golden Ratio x 1 = 1 x 1

8 Golden Ratio x 1 = 1 x 1 x(x 1) = 1 x2 x = 1 x2 x 1 = x=, 2 2 x 1+ 5 φ= =x=

9 Mona Lisa

10 Mona Lisa

11 Parthenon

12 Parthenon

13 Parthenon

14 Great Pyramid of Giza

15 Great Pyramid of Giza

16 Great Pyramid of Giza

17 Great Pyramid of Giza

18 Great Pyramid of Giza b = 4810 a = 3780

19 Great Pyramid of Giza 0 c a = 3780 b = 4810

20 Great Pyramid of Giza c = a c a = 3780 b = 4810

21 Human Arm

22 Human Arm

23 Human Arm = 55

24 Earth / Moon Radii

25 Earth / Moon Radii Radius of Earth a = 3,959 miles a

26 Earth / Moon Radii Radius of Earth a = 3,959 miles Radius of Earth + Moon b = 5,039 miles b a

27 Earth / Moon Radii Radius of Earth a = 3,959 miles Radius of Earth + Moon b = 5,039 miles a2 + b2 = c2 c = 6,408 miles c b a

28 Earth / Moon Radii Radius of Earth a = 3,959 miles Radius of Earth + Moon b = 5,039 miles a2 + b2 = c2 c = 6,408 miles c 6, 408 = a 3, 959 c b a

29 Relative Mean Orbital Distances Planet Mean distance (million km) Relative mean (Mercury=1) Mercury Venus Earth Mars Ceres Jupiter Saturn 1, Uranus 2, Neptune 4, Pluto 5,

30 Relative Mean Orbital Distances Planet Mean distance (million km) Relative mean (Mercury=1) Mercury Venus Earth Mars Ceres Jupiter Saturn 1, Uranus 2, Neptune 4, Pluto 5, Average 1,

31 Fibonacci Squares 1

32 Fibonacci Squares 1 1

33 Fibonacci Squares 2 1 1

34 Fibonacci Squares

35 Fibonacci Squares

36 Fibonacci Squares

37 Fibonacci Squares

38 Fibonacci Squares

39 Fibonacci Squares

40 Fibonacci Sequence Fn = {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,...}

41 Fibonacci Sequence Fn = {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,...} Fn+1 = Fn ,,,,,,,,,,,,

42 Fibonacci Sequence Fn = {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,...} Fn+1 = Fn ,,,,,,,,,,,, Fn+1 lim n F n 1+ 5 =φ=

43 Finger Bones

44 Finger Bones

45 Finger Bones

46 Human Arm = 55

47 Noah s Ark Make for yourself an ark of gopher wood; you shall make the ark with rooms, and shall cover it inside and out with pitch. This is how you shall make it: the length of the ark three hundred cubits, its breadth fifty cubits, and its height thirty cubits. Genesis 6:14-15 (NAS)

48 Noah s Ark Make for yourself an ark of gopher wood; you shall make the ark with rooms, and shall cover it inside and out with pitch. This is how you shall make it: the length of the ark three hundred cubits, its breadth fifty cubits, and its height thirty cubits. Genesis 6:14-15 (NAS) 50 5 =

49 Ark of the Covenant They shall construct an ark of acacia wood two and a half cubits long, and one and a half cubits wide, and one and a half cubits high. You shall overlay it with pure gold, inside and out you shall overlay it, and you shall make a gold molding around it. You shall cast four gold rings for it and fasten them on its four feet, and two rings shall be on one side of it and two rings on the other side of it. You shall make poles of acacia wood and overlay them with gold. You shall put the poles into the rings on the sides of the ark, to carry the ark with them. The poles shall remain in the rings of the ark; they shall not be removed from it. You shall put into the ark the testimony which I shall give you. Exodus 25:10-16 (NAS)

50 Ark of the Covenant

51 Ark of the Covenant

52 Ark of the Covenant =

53 Bronze Alter And you shall make the altar of acacia wood, five cubits long and five cubits wide; the altar shall be square, and its height shall be three cubits. You shall make its horns on its four corners; its horns shall be of one piece with it, and you shall overlay it with bronze. Exodus 27:1-2 (NAS)

54 Flower Petals Calla Lily 1 Petal

55 Flower Petals Euphorbia 2 Petals

56 Flower Petals Iris 3 Petals

57 Flower Petals Columbine 5 Petals

58 Flower Petals Bloodroot 8 Petals

59 Flower Petals Black-eyed Susan 13 Petals

60 Flower Petals African Daisy 21 Petals

61 Flower Petals Shasta Daisy 34 Petals

62 Flower Petals Michaelmas Daisy 55 Petals

63 Golden Spiral

64 Golden Spiral

65 Golden Spiral

66 Golden Spiral

67 Golden Spiral

68 Golden Spiral

69 Golden Spiral

70 Golden Spiral

71 Golden Spiral

72 Golden Spiral

73 Golden Spiral

74 Golden Spiral

75 Golden Spiral

76 Golden Spiral

77 Golden Spiral

78 Golden Spiral

79 Golden Spiral

80 Golden Spiral

81 Golden Spiral

82 Golden Spiral

83 Golden Spiral

84 Golden Spiral

85 Golden Spiral

86 Nautilus Shell

87 Nautilus Shell

88 Bighorn Sheep

89 Bighorn Sheep

90 Sunflower

91 Sunflower

92 Sunflower

93 Sunflower

94 Sunflower Counterclockwise Spirals

95 Sunflower

96 Sunflower

97 Sunflower Clockwise Spirals

98 Human Ear

99 Human Ear

100 Human Ear

101 Hurricane Isaac

102 Andromeda Galaxy

103 Andromeda Galaxy

104 Creation Reveals God For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. Romans 1:20

105