golden ratio, fibonacci numbers, and the golden spiraltlhiv.org/tmp/goldenratio.pdf · creation...

Golden Ratio, FibonacciNumbers, and the

Golden Spiral

by

Troy Henderson

University of Mobile

Creation Reveals GodGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

The heavens are telling of the glory of God; and their expanseis declaring the work of His hands. Day to day pours forthspeech, and night to night reveals knowledge. There is nospeech, nor are there words; Their voice is not heard. Theirline has gone out through all the earth, and their utterances tothe end of the world.

Psalm 19:1- 4a (NAS)

Golden RectangleGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson


1x 1

1 1

x


1x 1

1 1

x

x1=

1x 1

Golden RatioGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

x1=

1x 1

x(x 1) = 1x2 x = 1

x2 x 1 = 0

x =1 +

5

2,1

5

2

=x1= x =

1 +

52

1.618

Mona LisaGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

ParthenonGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Great Pyramid of GizaGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson


a = 378

b = 481


a = 378

b = 481c 611.75


a = 378

b = 481c 611.75

ca=

611.75378

1.618

Human ArmGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson


67

8

111

8


67

8

111

8

111

8

67

8

=

89

55 1.618

Earth / Moon RadiiGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Radius of Earth

a = 3,959 miles

Radius of Earth + Moonb = 5,039 miles

a2 + b2 = c2

c = 6,408 miles

ca=

6,4083,959

1.618

a

b c


Radius of Earth

a = 3,959 miles


a2 + b2 = c2

c = 6,408 miles

ca=

6,4083,959

1.618

a

a

b c


Radius of Earth

a = 3,959 miles


a2 + b2 = c2

c = 6,408 miles

ca=

6,4083,959

1.618

a

b

a

b c


Radius of Earth

a = 3,959 miles


a2 + b2 = c2

c = 6,408 miles

ca=

6,4083,959

1.618

a

b c

a

b c


Radius of Earth

a = 3,959 miles


a2 + b2 = c2

c = 6,408 miles

ca=

6,4083,959

1.618

a

b c

Relative Mean Orbital DistancesGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Planet Mean distance (million km) Relative mean (Mercury=1)Mercury 57.91 1.00000Venus 108.21 1.86859Earth 149.60 1.38250Mars 227.92 1.52353Ceres 413.79 1.81552Jupiter 778.57 1.88154Saturn 1,433.53 1.84123Uranus 2,872.46 2.00377Neptune 4,495.06 1.56488Pluto 5,869.66 1.30580

Average 1,640.67 1.61874

Relative Mean Orbital DistancesGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Planet Mean distance (million km) Relative mean (Mercury=1)Mercury 57.91 1.00000Venus 108.21 1.86859Earth 149.60 1.38250Mars 227.92 1.52353Ceres 413.79 1.81552Jupiter 778.57 1.88154Saturn 1,433.53 1.84123Uranus 2,872.46 2.00377Neptune 4,495.06 1.56488Pluto 5,869.66 1.30580Average 1,640.67 1.61874

Fibonacci SquaresGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

1


11


112


112

3


112

3 5


112

3 5

8


112

3 5

813


112

3 5

813

21


112

3 5

813

21 34

Fibonacci SequenceGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

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

Fn+1Fn

={

11,21,32,53,85,138,2113

,3421

,5534

,8955

,14489

,233144

, . . .}

limn

Fn+1Fn

= =1 +

5

2 1.618

Finger BonesGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

8

5

32


67

8

111

8

111

8

67

8

=

89

55

Noahs ArkGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Make for yourself an ark of gopher wood; you shall make theark with rooms, and shall cover it inside and out with pitch. Thisis how you shall make it: the length of the ark three hundredcubits, its breadth fifty cubits, and its height thirty cubits.

Genesis 6:14-15 (NAS)

5030

=53 1.66

Ark of the CovenantGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

They shall construct an ark of acacia wood two and a half cubitslong, and one and a half cubits wide, and one and a half cubitshigh. You shall overlay it with pure gold, inside and out you shalloverlay it, and you shall make a gold molding around it. You shallcast four gold rings for it and fasten them on its four feet, and tworings shall be on one side of it and two rings on the other side ofit. 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 carrythe ark with them. The poles shall remain in the rings of the ark; theyshall not be removed from it. You shall put into the ark the testimonywhich I shall give you.

Exodus 25:10-16 (NAS)


212

112

212112

=53

Bronze AlterGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

And you shall make the altar of acacia wood, five cubits longand five cubits wide; the altar shall be square, and its heightshall be three cubits. You shall make its horns on its fourcorners; its horns shall be of one piece with it, and you shalloverlay it with bronze.

Exodus 27:1-2 (NAS)

Flower PetalsGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Calla Lily

1 Petal


Euphorbia

2 Petals


Iris

3 Petals


Columbine

5 Petals


Bloodroot

8 Petals


Black-eyed Susan

13 Petals


African Daisy

21 Petals


Shasta Daisy

34 Petals


Michaelmas Daisy

55 Petals

Golden SpiralGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Nautilus ShellGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Bighorn SheepGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

SunflowerGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson


1 2 34

56

78910

11

1213

1415

161718192021

2223

2425

26

27

2829

3031

3233 34

34 Counterclockwise Spirals


1 2 3

4

5

6

7

8

91011

12

1314

15

16

17

1819

2021

21 Clockwise Spirals

Human EarGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Hurricane IsaacGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Andromeda GalaxyGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

Creation Reveals GodGolden Ratio, Fibonacci Numbers, and the Golden Spiral Troy Henderson

For since the creation of the world His invisible attributes, Hiseternal power and divine nature, have been clearly seen,being understood through what has been made, so that theyare without excuse.

Romans 1:20

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