Nature loves symmetry... there are patterns and proportions all around us, that make sense of this whole chaos of the world, we live in... i remember how i felt when i came to know of pi, it felt like in some mysterious way, everything has an inherent nature of being pre-defined... that theres an order of things, that we just have to decipher and everything would be simplified to plain mathematics and logic..
Phi is another such number... better known as golden ratio; its been there consistently, just under our eyes, in nature, in architecture, in paintings, in music, in beauty and even in your DNA...heres a nice video about phi...
So, two quantities are said to be in golden ratio if, the ratio of their sum to the larger quantity is equal to the ratio of the larger one to the smaller one..
or (a+b)/a=a/b=phi (if 'a' is the larger one and 'b' is the smaller one)
or a=(phi)b
substituting this value of phi in first equation yields
phi=(1+sqrt(5))/2=1.6180339887....
Some unique things about phi::
* the ratio of subsequent numbers in fibonacci series tends to phi:
21/13 = 1.61538...
34/21 = 1.61905...
55/34 = 1.61764...
89/55 = 1.61861...
* 1/1.618=0.618, the golden ratio conjugate
* (sqrt(5) + 1)/2=1.618 and (sqrt(5) - 1)/2=0.618
* phi^(n+2)=phi^(n+1) + phi^(n); i.e. the powers of phi have this unusual property in that they are related not only exponentially, but are additive as well
* The human body conforms to phi...
-The distance between the finger tip and the elbow / distance between the wrist and the elbow,
-The distance between the shoulder line and the top of the head / head length,
-The distance between the navel and the top of the head / the distance between the shoulder line and the top of the head,
-The distance between the navel and knee / distance between the knee and the end of the foot,
-Length of face / width of face,
-Distance between the lips and where the eyebrows meet / length of nose,
-Length of face / distance between tip of jaw and where the eyebrows meet,
-Length of mouth / width of nose,
-Width of nose / distance between nostrils,
-Distance between pupils / distance between eyebrows.
in Architechture
The Golden Ratio has appeared in ancient architecture. The examples are many, such as the Great Pyramid in Giza, Egypt, and the Greek Parthenon that was constructed between 447 and 472BC. Not only did the ancient Egyptians and Greeks know about the magic of Golden Ratio, so did the Renaissance artists, who used it in the design of Notre Dame in between the 12th and 14th centuries. Some modern architecture are also influenced by Golden Ratio as well, such as the United Nations Building...
in DNA
The DNA molecule, the very program of life, is based on the golden ratio. DNA consists of two intertwined perpendicular helixes. The length of the curve in each of these helixes is 34 angstroms and the width 21 angstroms. Also, the major and minor groove of B-DNA follow golden ratio...
in Art
Da Vinci, a sculpture, painter, inventor and a mathematician, was the first one who first called Phi the Golden Ratio. And scientifically, Mona Lisa's face actually appears in a golden rectangle, which also makes her face appear more beautiful to human eyes. Also another masterpiece, the Last Supper, contains Golden Ratios...
....now, the list is practically endless, so i better stop here...
Conclusion: the golden ratio is ruling the world...watch this clip from "Numbers" where Charlie talks about golden ratio...
Phi is another such number... better known as golden ratio; its been there consistently, just under our eyes, in nature, in architecture, in paintings, in music, in beauty and even in your DNA...heres a nice video about phi...
So, two quantities are said to be in golden ratio if, the ratio of their sum to the larger quantity is equal to the ratio of the larger one to the smaller one..
or (a+b)/a=a/b=phi (if 'a' is the larger one and 'b' is the smaller one)
or a=(phi)b
substituting this value of phi in first equation yields
phi=(1+sqrt(5))/2=1.6180339887....
Some unique things about phi::
* the ratio of subsequent numbers in fibonacci series tends to phi:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
13/8 = 1.6252/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
21/13 = 1.61538...
34/21 = 1.61905...
55/34 = 1.61764...
89/55 = 1.61861...
* 1/1.618=0.618, the golden ratio conjugate
* (sqrt(5) + 1)/2=1.618 and (sqrt(5) - 1)/2=0.618
* phi^(n+2)=phi^(n+1) + phi^(n); i.e. the powers of phi have this unusual property in that they are related not only exponentially, but are additive as well
* The human body conforms to phi...
-The distance between the finger tip and the elbow / distance between the wrist and the elbow,
-The distance between the shoulder line and the top of the head / head length,
-The distance between the navel and the top of the head / the distance between the shoulder line and the top of the head,
-The distance between the navel and knee / distance between the knee and the end of the foot,
-Length of face / width of face,
-Distance between the lips and where the eyebrows meet / length of nose,
-Length of face / distance between tip of jaw and where the eyebrows meet,
-Length of mouth / width of nose,
-Width of nose / distance between nostrils,
-Distance between pupils / distance between eyebrows.
in Architechture
The Golden Ratio has appeared in ancient architecture. The examples are many, such as the Great Pyramid in Giza, Egypt, and the Greek Parthenon that was constructed between 447 and 472BC. Not only did the ancient Egyptians and Greeks know about the magic of Golden Ratio, so did the Renaissance artists, who used it in the design of Notre Dame in between the 12th and 14th centuries. Some modern architecture are also influenced by Golden Ratio as well, such as the United Nations Building...
in DNA
The DNA molecule, the very program of life, is based on the golden ratio. DNA consists of two intertwined perpendicular helixes. The length of the curve in each of these helixes is 34 angstroms and the width 21 angstroms. Also, the major and minor groove of B-DNA follow golden ratio...
in Art
Da Vinci, a sculpture, painter, inventor and a mathematician, was the first one who first called Phi the Golden Ratio. And scientifically, Mona Lisa's face actually appears in a golden rectangle, which also makes her face appear more beautiful to human eyes. Also another masterpiece, the Last Supper, contains Golden Ratios...
....now, the list is practically endless, so i better stop here...
Conclusion: the golden ratio is ruling the world...watch this clip from "Numbers" where Charlie talks about golden ratio...
1 comment:
"bravo" for your nice golden ratio site
please
about golden ratio and dna:
http://golden-ratio-in-dna.blogspot.com/
Post a Comment