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The Late Show...With Your Host, Cena

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Groucho said:
Do you mean that Fibonacci sequence? Spirals and all that.
Click to expand...

Yeah I think there's bit more to it than that. This is the best I could about it

Life and the Golden Ratio

There are many other fascinating mathematical relationships and oddities in both Phi and the Fibonacci series that can be explored in more depth, but for now let’s now take a step away from the purely mathematical and venture into nature, where Phi and the Fibonacci series manifest themselves pervasively, but not universally. Fibonacci numbers frequently appear in the numbers of petals in a flower. The positions and proportions of the key dimensions of many, if not most, animals are based on Phi. Examples include the body sections of ants and other insects, the wing dimensions and location of eye-like spots on moths, the spirals of sea shells and the position of the dorsal fins on porpoises. Even the spirals of human DNA embody phi proportions. More intriguing yet is the extensive appearance of Phi throughout the human form, in the face, body, fingers, teeth and even our DNA, and the impact that this has on our perceptions of human beauty.

Some would argue that beauty is in the eye of the beholder, but there is sound basis in scientific study and evidence to support that what we perceive as beauty in both men and women is based on how closely the proportions of facial and body dimensions come to Phi. It seems that Phi is hard-wired into our consciousness as a guide to beauty. For this reason, Phi is applied in both facial plastic surgery and cosmetic dentistry as a guide to achieving the most natural and beautiful results in facial features and appearance.

Art, Architecture and Design

With all the unique mathematical properties of Phi and its appearance throughout creation, it’s little wonder that mankind would not only take notice of this number and the Golden Ratio it creates, but also use it to capture the beauty and harmony of nature in our own creations in art, architecture and other areas of design. In some cases, mankind’s application of Phi is undeniable. In other cases, it is still the subject of debate. The Great Pyramid of Egypt appears to embody the Golden Ratio in the ratios of its base, height and hypotenuse, but its state of ruin and the absence of the mention of Phi in ancient Egyptian writings make it difficult to prove conclusively that this was by design. Since the Greeks knew of Phi at the time of the building of the Parthenon, it seems quite clear to many that the Golden Ratio relationships found therein were by design, yet the evidence is not complete and there are those who contest this as well. It is recognized that Leonardo Da Vinci used Phi, known in the 1500’s as “The Divine Proportion,” in a number of his paintings. While this is undeniable, some see Phi relationships where others do not believe they were intended. The dimensions of the treasured Stradivarius violinsbuilt around 1700 show clear Phi relationships. It plays a role in music and acoustics. More modern applications of the Golden Ratio in architecture can be seen in Notre Dame in Paris, the United Nations building in New York and the CN Tower in Toronto. It’s commonly used in the design of products and logos and by many major corporations. It’s even being used in high fashion clothing design in the “Phi Collection” announced in 2004 and covered by Vogue, Elle and Vanity Fair.

New Discoveries involving the Golden Ratio

The Golden Ratio continues to open new doors in our understanding of life and the universe. It appeared in Roger Penrose’s discovery in the 1970′s of “Penrose Tiles,” which allowed surfaces to be tiled in five-fold symmetry, a task previously thought impossible. It appeared again in the 1980′s in the three-dimensional molecular arrangement of quasi-crystals, a newly discovered form of matter. As we enter the 21st century, Phi seems to be having a rebirth in integrating knowledge across a wide variety of fields of study, including time and quantum physics.

Spiritual Aspects

The description of this golden proportion as the Divine proportion is perhaps fitting because it is seen by many as a door to a deeper understanding of beauty and spirituality in life, unveiling a hidden harmony or connectedness in so much of what we see. That’s an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the foundations of life itself. The line between its mathematical and mystical aspects is thus not easily drawn. Phi does not appear explicitly in the Bible or other ancient scriptures, yet we find that the dimensions given by God to Noah for the Ark and to Moses for the Ark of the Covenant both reflect a 5 to 3 proportion, Fibonacci numbers with a ratio of 1.666, and a reasonably close approximation to Phi. The Kaaba, the most sacred site of Islam in Mecca, is located very close to the golden ratio of the distance between the Earth’s north and south poles. Curiously enough, even the symbol for Phi, a circle with a line drawn through it, can be thought to represent a zero, or void, divided by one, or Unity, to create beauty, analogous to God creating the universe from nothing.

A Journey of Discovery

In matters of reason, seeing is believing but in matters of faith, it is believing that first opens the door to seeing. Just as we need two eyes to add depth to our perception in vision, both faith and reason serve us in adding depth to our understanding of life and the universe in which we live. The best way to know for yourself where Phi is present and where it is imagined is to explore with an open mind, learn and reach your own conclusions. You can learn more about the Golden Ratio here at www.GoldenNumber.net and download PhiMatrix golden ratio design software at www.phimatrix.com to easily discover and apply Phi proportions for yourself. Enjoy the “phi”nomemon, whether to enhance your own understanding and appreciation of beauty and harmony in life or to apply it to your own artistic creations, like Leonardo Da Vinci and other masters before you. You may contribute your own insights and findings to share with our online community.
 
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steken1 said:
Yeah I think there's bit more to it than that. This is the best I could about it

Life and the Golden Ratio

There are many other fascinating mathematical relationships and oddities in both Phi and the Fibonacci series that can be explored in more depth, but for now let’s now take a step away from the purely mathematical and venture into nature, where Phi and the Fibonacci series manifest themselves pervasively, but not universally. Fibonacci numbers frequently appear in the numbers of petals in a flower. The positions and proportions of the key dimensions of many, if not most, animals are based on Phi. Examples include the body sections of ants and other insects, the wing dimensions and location of eye-like spots on moths, the spirals of sea shells and the position of the dorsal fins on porpoises. Even the spirals of human DNA embody phi proportions. More intriguing yet is the extensive appearance of Phi throughout the human form, in the face, body, fingers, teeth and even our DNA, and the impact that this has on our perceptions of human beauty.

Some would argue that beauty is in the eye of the beholder, but there is sound basis in scientific study and evidence to support that what we perceive as beauty in both men and women is based on how closely the proportions of facial and body dimensions come to Phi. It seems that Phi is hard-wired into our consciousness as a guide to beauty. For this reason, Phi is applied in both facial plastic surgery and cosmetic dentistry as a guide to achieving the most natural and beautiful results in facial features and appearance.

Art, Architecture and Design

With all the unique mathematical properties of Phi and its appearance throughout creation, it’s little wonder that mankind would not only take notice of this number and the Golden Ratio it creates, but also use it to capture the beauty and harmony of nature in our own creations in art, architecture and other areas of design. In some cases, mankind’s application of Phi is undeniable. In other cases, it is still the subject of debate. The Great Pyramid of Egypt appears to embody the Golden Ratio in the ratios of its base, height and hypotenuse, but its state of ruin and the absence of the mention of Phi in ancient Egyptian writings make it difficult to prove conclusively that this was by design. Since the Greeks knew of Phi at the time of the building of the Parthenon, it seems quite clear to many that the Golden Ratio relationships found therein were by design, yet the evidence is not complete and there are those who contest this as well. It is recognized that Leonardo Da Vinci used Phi, known in the 1500’s as “The Divine Proportion,” in a number of his paintings. While this is undeniable, some see Phi relationships where others do not believe they were intended. The dimensions of the treasured Stradivarius violinsbuilt around 1700 show clear Phi relationships. It plays a role in music and acoustics. More modern applications of the Golden Ratio in architecture can be seen in Notre Dame in Paris, the United Nations building in New York and the CN Tower in Toronto. It’s commonly used in the design of products and logos and by many major corporations. It’s even being used in high fashion clothing design in the “Phi Collection” announced in 2004 and covered by Vogue, Elle and Vanity Fair.

New Discoveries involving the Golden Ratio

The Golden Ratio continues to open new doors in our understanding of life and the universe. It appeared in Roger Penrose’s discovery in the 1970′s of “Penrose Tiles,” which allowed surfaces to be tiled in five-fold symmetry, a task previously thought impossible. It appeared again in the 1980′s in the three-dimensional molecular arrangement of quasi-crystals, a newly discovered form of matter. As we enter the 21st century, Phi seems to be having a rebirth in integrating knowledge across a wide variety of fields of study, including time and quantum physics.

Spiritual Aspects

The description of this golden proportion as the Divine proportion is perhaps fitting because it is seen by many as a door to a deeper understanding of beauty and spirituality in life, unveiling a hidden harmony or connectedness in so much of what we see. That’s an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the foundations of life itself. The line between its mathematical and mystical aspects is thus not easily drawn. Phi does not appear explicitly in the Bible or other ancient scriptures, yet we find that the dimensions given by God to Noah for the Ark and to Moses for the Ark of the Covenant both reflect a 5 to 3 proportion, Fibonacci numbers with a ratio of 1.666, and a reasonably close approximation to Phi. The Kaaba, the most sacred site of Islam in Mecca, is located very close to the golden ratio of the distance between the Earth’s north and south poles. Curiously enough, even the symbol for Phi, a circle with a line drawn through it, can be thought to represent a zero, or void, divided by one, or Unity, to create beauty, analogous to God creating the universe from nothing.

A Journey of Discovery

In matters of reason, seeing is believing but in matters of faith, it is believing that first opens the door to seeing. Just as we need two eyes to add depth to our perception in vision, both faith and reason serve us in adding depth to our understanding of life and the universe in which we live. The best way to know for yourself where Phi is present and where it is imagined is to explore with an open mind, learn and reach your own conclusions. You can learn more about the Golden Ratio here at www.GoldenNumber.net and download PhiMatrix golden ratio design software at www.phimatrix.com to easily discover and apply Phi proportions for yourself. Enjoy the “phi”nomemon, whether to enhance your own understanding and appreciation of beauty and harmony in life or to apply it to your own artistic creations, like Leonardo Da Vinci and other masters before you. You may contribute your own insights and findings to share with our online community.
Click to expand...


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