Embed Size (px)
DESCRIPTION
Citation preview
Math – The Language of God
Miracles of Numbers
Math – The Language of God
Miracles of Numbers
Can you guess the next number in this sequence?
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
23389 + 144 =
FIBONACCI’S SEQUENCEThis sequence of numbers was first discovered in the 12th century, by the Italian mathematician, Leonardo Fibonacci, and hence is known as Fibonacci's Sequence.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
1
1 1.0000000000000000
2 2.0000000000000000
3 1.5000000000000000
5 1.6666666666666700
8 1.6000000000000000
13 1.6250000000000000
21 1.6153846153846200
34 1.6190476190476200
55 1.6176470588235300
89 1.6181818181818200
144 1.6179775280898900
233 1.6180555555555600
377 1.6180257510729600
610 1.6180371352785100
987 1.6180327868852500
1,597 1.6180344478216800
2,584 1.6180338134001300
4,181 1.6180340557275500
6,765 1.6180339631667100
10,946 1.6180339985218000
17,711 1.6180339850173600
28,657 1.6180339901756000
46,368 1.6180339882053200
75,025 1.6180339889579000
• This ratio is called the Golden Ratio or the number is called Phi – Sacred Cut, Divine Proportion
Now why is this ratio called he Divine Proportion?
Because a lot of things in nature occur in this Ratio or in the Fibonacci Sequence..
LETS TAKE A LOOK AT THE DIMENSIONS OF THE DNA
DNA molecule—contains the golden ratio. One revolution of the double helix measures 34 angstroms while the width is 21 angstroms. The ratio 34/21 reflects phi 34 divided by 21 equals 1.619… a close approximation of phi’s 1.618.
13
Fibonacci numbers can be found in many places, for example the number of petals on a flower is often a Fibonacci number.
1
532
21138
People wonder…
Why is that the number of petals in a flower is often one of the following numbers:
3,5,8,13,21,34,55?
Branching Plants
• Leaves are also found in groups of Fibonacci numbers.
• Branching plants always branch off into groups of Fibonacci numbers.
Golden Ration in the Human Body
Video
The Golden Rectangle
:
The perfect rectangle?
So, why do shapes that exhibit the Golden Ratio seem more appealing to the human eye? No one really knows for sure. But we do have
evidence that the Golden Ratio seems to be Nature's perfect number.
The front two incisor teeth form a golden rectangle, with a phi ratio in the height to the width. The ratio of the width of the first tooth to the second tooth from the center is also phi.The ratio of the width of the smile to the third tooth from the center is phi as well.
GOLDEN RATIO IN ART & ARCHITECTURE
23
The Golden Rectangle in Art & Architecture
Secret to aesthetics, Inspired by Nature
Video
• Gauge
The Golden Spiral
EXERCISE
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
39
YOU HAVE JUST MADE AN ATTEMPT TO FORGE THE SIGNATURE OF GOD
THIS IS CALLED THE GOLDEN SPIRAL AND IS SEEN IN MANY ASPECTS OF NATURE
42
Chameleon's tail
The chambered nautilus
Sunflower petals follow the Fibonacci Sequence and Sunflower Seeds follow the Golden Spiral
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Low pressure system over Iceland filmed from a satellite
A Sea Shell
A cacti with multiple Fibonacci-like Spirals.
Spiral galaxies
The natural growth of this plant is similar to a Fibonnaci Spiral
Cauliflower Pine cone
Video
Tying it back to the beginning
Thank You!
