Is God a Mathematician?
It may be mere coincidence, but the number 1.61803 has been popping up everywhere - from art to mathematics to science to nature and beyond. Nobody exactly knows what makes this number so special, but its mere impact on everything we see, touch, feel, taste, and hear should be proof enough of its importance.
Once denoted by the Greek letter tau (now represented by the Greek letter phi), this number is often referred to as the "golden ratio" - and some call it the "divine ratio" or "divine proportion," given its unique properties and prevalence in nature.
Euclid first defined the "divine proportion" in 300 B.C. as the ratio produced when a "whole line is to the greater segment, as the greater is to the less." In other words, assuming a line segment ACB, the divine ratio is the ratio at which AC/CB = AB/AC. Specifically, the ratio equals 0.5 *(1+sqrt(5)), or approximately 1.61803.
Since Euclid's accidental discovery, this ratio has appeared in many unexpected places, leading biologists, artists, musicians, historians, architects, psychologists, and even mystics to ponder on its ubiquity and appeal. Intellectuals have attempted to uncover the meaning behind this "golden ratio" for the past 2,400 years, but to this day, more is known about where it exists, than why it exists.
Below are some places where the "divine ratio" is found:
Mathematics
Fibonacci Sequence - A Fibonacci sequence is constructed by summing the two preceding numbers to produce the next number. The divine ratio is used to calculate the nth number in a Fibonacci sequence.
Trigonometry - The trigonometric functions (and natural logs) can be defined using the "divine ratio."
Biology
Human Heartbeat - The human heartbeat is often considered to be an integral part of the human soul. It has been shown that a heartbeat that follows the "divine ratio" represents a state of health, peace, and harmony."
Human anatomy - Each section of your index finger is proportionately larger than the preceding one by the "divine ratio." The ratio of your forearm to your hand is also the "divine ratio." Your feet follow the divine ratio: 1) the middle arch of the foot 2) the widest part of the foot 3) the base oft the toe line and the big toe. And it doesn't stop at that - your body, your face, even your teeth follow the divine ratio!
DNA - The double helix of a DNA molecule follows the "divine ratio."
Nature - The spiral of sea shells, the eye-like markings of moths, and even the dimensions of a dolphin's body follow the "divine ratio." This can be applied to all other types of fish, birds, mammals, and insects.
Plants - Flower petals, fruit seed, and tree branches have been shown to follow the "divine ratio."
Art
Beauty - De Divina Proportione by Luca Pacioli, a three-volume work published in 1509 suggests the golden ratio's application yields pleasing, harmonious proportions, which we interpret as beauty.
Architecture - Studies show the Parthenon and the Great Mosque of Kairouan's proportions approximate the "divine ratio."
Painting - The "divine ratio" was employed in Leonardo da Vinci's illustrations in De Divina Proportione and the Mona Lisa, Salvador DalÃ's The Sacrament of the Last Supper, many of Mondrian's works.
Music
Music - The "divine ratio" appears in a variety of works, including Debussy's Image, Reflections in Water.
Stock Market
Technical Analysis - Elliott Wave Theory uses the "divine ratio" to predict up and down movements in the stock market.
Astronomy
Space - Anything from the distance between planets, to the structure of Saturn's rings relates to the "divine ratio."
In many ways, the "divine ratio" seems way too methodical to be random. It provides a sort of harmonious predictability in a world where things are often times considered to be unorganized and chaotic. It also unifies us all. Perhaps this is part of the divine message: we all come from the same place. We may never fully understand the relevance behind the actual number itself, but the beauty that manifests itself from this ratio is truly "divine" - and it doesn't take much brain power to see that...
Once denoted by the Greek letter tau (now represented by the Greek letter phi), this number is often referred to as the "golden ratio" - and some call it the "divine ratio" or "divine proportion," given its unique properties and prevalence in nature.
Euclid first defined the "divine proportion" in 300 B.C. as the ratio produced when a "whole line is to the greater segment, as the greater is to the less." In other words, assuming a line segment ACB, the divine ratio is the ratio at which AC/CB = AB/AC. Specifically, the ratio equals 0.5 *(1+sqrt(5)), or approximately 1.61803.
Since Euclid's accidental discovery, this ratio has appeared in many unexpected places, leading biologists, artists, musicians, historians, architects, psychologists, and even mystics to ponder on its ubiquity and appeal. Intellectuals have attempted to uncover the meaning behind this "golden ratio" for the past 2,400 years, but to this day, more is known about where it exists, than why it exists.
Below are some places where the "divine ratio" is found:
Mathematics
Fibonacci Sequence - A Fibonacci sequence is constructed by summing the two preceding numbers to produce the next number. The divine ratio is used to calculate the nth number in a Fibonacci sequence.
Trigonometry - The trigonometric functions (and natural logs) can be defined using the "divine ratio."
Biology
Human Heartbeat - The human heartbeat is often considered to be an integral part of the human soul. It has been shown that a heartbeat that follows the "divine ratio" represents a state of health, peace, and harmony."
Human anatomy - Each section of your index finger is proportionately larger than the preceding one by the "divine ratio." The ratio of your forearm to your hand is also the "divine ratio." Your feet follow the divine ratio: 1) the middle arch of the foot 2) the widest part of the foot 3) the base oft the toe line and the big toe. And it doesn't stop at that - your body, your face, even your teeth follow the divine ratio!
DNA - The double helix of a DNA molecule follows the "divine ratio."
Nature - The spiral of sea shells, the eye-like markings of moths, and even the dimensions of a dolphin's body follow the "divine ratio." This can be applied to all other types of fish, birds, mammals, and insects.
Plants - Flower petals, fruit seed, and tree branches have been shown to follow the "divine ratio."
Art
Beauty - De Divina Proportione by Luca Pacioli, a three-volume work published in 1509 suggests the golden ratio's application yields pleasing, harmonious proportions, which we interpret as beauty.
Architecture - Studies show the Parthenon and the Great Mosque of Kairouan's proportions approximate the "divine ratio."
Painting - The "divine ratio" was employed in Leonardo da Vinci's illustrations in De Divina Proportione and the Mona Lisa, Salvador DalÃ's The Sacrament of the Last Supper, many of Mondrian's works.
Music
Music - The "divine ratio" appears in a variety of works, including Debussy's Image, Reflections in Water.
Stock Market
Technical Analysis - Elliott Wave Theory uses the "divine ratio" to predict up and down movements in the stock market.
Astronomy
Space - Anything from the distance between planets, to the structure of Saturn's rings relates to the "divine ratio."
In many ways, the "divine ratio" seems way too methodical to be random. It provides a sort of harmonious predictability in a world where things are often times considered to be unorganized and chaotic. It also unifies us all. Perhaps this is part of the divine message: we all come from the same place. We may never fully understand the relevance behind the actual number itself, but the beauty that manifests itself from this ratio is truly "divine" - and it doesn't take much brain power to see that...
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