OnceByten
09-24-2004, 08:13 PM
I hope this is the right forum for this...
There is a special ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies.
Think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. When you have written down about 20 numbers, calculate the ratio of the last to the second from last. The answer should be close to 1.6180339887...
What's the significance of this number? It's the "golden ratio" and, arguably, it crops up in more places in art, music and so on than any number except pi. Claude Debussy used it explicitly in his music and Le Corbusier in his architecture. There are claims the number was used by Leonardo da Vinci in the painting of the Mona Lisa, by the Greeks in building the Parthenon and by ancient Egyptians in the construction of the Great Pyramid of Khufu.
The appeal of the divine proportion to the human eye and brain has been scientifically tested. Dozens of psychological tests, beginning with those of Gustav Fechner in the 19th century, have shown that, when subjects are presented with a range of rectangles, they invariably pick out as most pleasing ones whose sides are in the golden ratio.
But the most surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. Take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most com mon angle between successive leaves is 137.5 - the golden angle. Why? Because 137.5 = 360 - 360/G, where G is the golden ratio. Why does the golden ratio play a role in the arrangement of leaves? It's all down to the "irrationality" of the number. Irrational numbers are ones that cannot be expressed as the ratio of two whole numbers - for instance, 5/2.
Thoughts?
There is a special ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies.
Think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. When you have written down about 20 numbers, calculate the ratio of the last to the second from last. The answer should be close to 1.6180339887...
What's the significance of this number? It's the "golden ratio" and, arguably, it crops up in more places in art, music and so on than any number except pi. Claude Debussy used it explicitly in his music and Le Corbusier in his architecture. There are claims the number was used by Leonardo da Vinci in the painting of the Mona Lisa, by the Greeks in building the Parthenon and by ancient Egyptians in the construction of the Great Pyramid of Khufu.
The appeal of the divine proportion to the human eye and brain has been scientifically tested. Dozens of psychological tests, beginning with those of Gustav Fechner in the 19th century, have shown that, when subjects are presented with a range of rectangles, they invariably pick out as most pleasing ones whose sides are in the golden ratio.
But the most surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. Take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most com mon angle between successive leaves is 137.5 - the golden angle. Why? Because 137.5 = 360 - 360/G, where G is the golden ratio. Why does the golden ratio play a role in the arrangement of leaves? It's all down to the "irrationality" of the number. Irrational numbers are ones that cannot be expressed as the ratio of two whole numbers - for instance, 5/2.
Thoughts?