Would you please elucidate and elaborate it . Thank you so much ! At to A-qualit
ID: 3475558 • Letter: W
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Would you please elucidate and elaborate it . Thank you so much ! At to A-quality work 1. Now that you have been exposed to the "Golden Ratio" (Phi) relate it to something that interests you and write at least TWO PARAGRAPHS that explain the relationship in your own words. Then, turn those 2 paragraphs into a DIALOGUE between at least 2 characters where one is explaining it to the other. The dialogue sliould be long enough to fully explain the concept (I'd say at least most of a page, in "dramatic style" lines)Explanation / Answer
THE golden ratio is a special number found by dividing a line in to two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer period . it is often symbolized using phi, after the 21st letter of the greek alphabet . in an equation from, it looks like this :
a/b = (a+b)/a = 1.6180339887498948420.....
line segment in the golden ratio are a+b is to a as a is to b
as with pi ( the ratio of the circumferrence of a circle to its diameter), the digits go on and on,theoretically into infinity. phi is usally rounded off to 1.618. this number has been discovered many times,which is why it has so many names -- the golden mean, the golden section, divine proportion,etc,. historically the number can be seen in the architechure of many acient creations, like the great pyramids and the parthenon.
example: the graet pyramid of giza, the length of eachside of the base is 756 feet with a height 482feet. the ratio of the base to the height is roughly 1.5717, which is close to the golden ratio.
around 1200 , mathematician lenardo fibnacci discovered the unique properties of the fibonacci sequence. this squence ties directly in to the golden ratio ,because if you take any two succssive fibaconni numbers get higher ,the ratio becomes even closer to 1.618.
example: the ratio of 3 to 5 is 1.666.but the ratio of 13 to 21 is 1.625. getting even higher , the ratio of 144 to 233 is 1.618. these numbers are all successive numbers in the fibonacci sequence.
these numbers can be applied to the proportions of a rectangle, called golden rectangle , the appearence of the golden ratio is art . the golden rectangle is also related to the golden spiral, which is created by making adjacent squares of fibonacci dimensions.
lenardo da vinci 's 'vitruvian man' is said to illustrate the golden ratio.
the term ''phi'' was coined by american mathematician mark barr in the 1990s .phi has continued to appear in mathematicians and physics, including the 1970s penrosetiles,which allowed surfaces to be tiled in five-fold symmetry in the 1980s, phi appeared in quasi crystals, a then newly discovered form of matter .
phi is more than an obscure term found in mathematics and physics . it appears around us in our daily lives even in our aesthetic views.
the golden ratio also appears in all forms of nature and science . some unexpected places include:
flower petals : the no. of petals on some flowers follows the fibonacci sequence. it is belived that in the darwinian processes,each petal is placed to allow for the best possible exposure to sunlight and other factors.
seed heads: the seeds of a flower are often produced at the center and migrate outward to fill the space.
example, sunflowers follow this pattern
pinecones : the spiral pattern of the speed pods spiral upward in opposite directions. the no. of steps the spirals take tend to match fibonacci
tree branches : the way tree branches from or split is an example of the fibonacci sequence.
shells: many shells ,including snail shells and nautils shells,are perfect examples of the golden spiral.
spiral galaxy : the milky way has a number of spiral arms the shape of the spiral is identical to the golden spiral, and the golden rectangle can be drawn over any spiral galaxy
hurricanes: much like shells , hurricanes often display the golden spiral
fingers: the length of our fingers , each section from the tip of the base to the wrist is larger than the preceding one by roughly the ratio of phi.
animal bodies: the measurement of the human navel to the floor and the top of the head to the navel is the golden ratio.
DNA moleculeS: a dna molecule measures 34 angstorms by 21 angstorms at each full cycle of the diuble helix spiral. in the fibonacci series , 34 and 21 are successive numbers .
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