whats the golden ratio history??
923686
The golden ratio expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. The golden ratio is the following algebraic irrational number with its numerical approximation:
392007
When it began the ratio was 10 to 1.\nIn twenty years it will be approximately 3 to 1.\nI do not have the present ratio.
437
Well, many people answered the question. Fibonacci sequence starts from 0 and Nth Fibonacci Number is sum of (N-1) th and (N-2) th Fibonacci Number.\nSequence goes like 0,1,1,2,3,5,8,13,21,34…....\n\nIt is an empirical fact that the ratio of consecutive Fibonacci Numbers converges to an interesting value near to 1.6 called (to be accurate it is (1+SQRT (5))/2) golden ratio or golden mean.\nThere ere are some interesting facts about golden ratio:\n1.\nThe growth of nautilus shell, growth of populations and many other kinds of natural “growing,” are somehow governed by mathematical properties exhibited in the Fibonacci sequence. Not just the rate of growth, but the pattern of growth. Examine the crisscrossing spiral seed pattern in the head of a sunflower, for instance, and you will discover that the number of spirals in each direction is invariably two consecutive Fibonacci numbers.\n2. \nGolden ratio is related to construction of great ancient architectures like Great pyramids in Egypt. \nLink: http://www.dartmouth.edu/~matc/math5.geometry/unit2/unit2.html\n3.\nYou can follow this link for exploring its use in poetry, music, art and now a days it is used for stock market predictions as well. This link will tell you the origin of the word Fibonacci as well.\nLink: http://www2.evansville.edu/studiochalkboard/cm-fibonacci.html
1157451
Gold's density is:\n\n19, 320 kg/m^3\n\nVolume of the bar is:\n\nV = 5 inches^3\n\n5 inches^3 = 8.19 x 10^-5 m^3\n\nThen: 19,320 kg/m^3 = x kg/[8.19 x 10^-5 m^3]\n\nSo, x = 1.58 kg, or 3.5 lbs.\n\nBeyond the facts you gave I couldn't tell you what the gold bars were actually like at that time....sorry.
960068
golden eagle day represents pay day. i.e. the golden eagle shits  ( gold ) to-day
954856
mean is 85/3, or 28.33333......\n\ni dont know, its just always been that way
1161642
It's approximately equal to 1.61803398874989...,\nand is equal to [1 + sq.rt.(5)] / 2.\n\nThe ancient Greeks thought it was divine because the ratio of 1:1.618... provided what they termed the perfect rectangle in architecture.  The ratio 1:1.618... is equal to 0.618...:1\n\nMathematically, it's the only number that when squared is one more than itself.  \n1.61803398874989... * 1.61803398874989... = 2.61803398874989...,\nthough the numbers are irrational, continuing infininely with no repeating pattern.\n\nThe ratio appears in regular pentagons (starfish), Archimedean spirals (seashells), and in DaVinci's proportions in drawing the human figure.\n\n[Edited to comment]\nAll of jalonzmommy's crap doesn't answer the question asked.\nAlso, check out http://en.wikipedia.org/wiki/Golden_ratio
829782
http://en.wikipedia.org/wiki/Gold\n\nWikipedia is a good place to start
661146
Phi, or the Golden Ratio, appears in many paintings and pieces of architecture. Da Vinci, for example, claimed it was the "perfect proportion" so he used it in many of his paintings (and also showed that many parts of the body follow this ratio). In that aspect, yes, some people have argued it might be the "most attractive number", or better to say "most attractive ratio".
644837
ummm isnt it 1.1816...? no, thats not it...well its sometihng like that, and its found in nature everywhere. I think it was in the davinci code, too. But its like the "perfect number" and i had to watch a movie on it during math.
99187
This was a form of math that gained a small following several years ago with the Hmong of Thiland. It's not used very much today due to its limited application.   Edited comment:  Pastor Dave is correct, it's still used. I think it was also used for a few months at Enron, Corp.
351788
The Fibonacci series has a number of interesting properties.\n\nThe ratio of successive terms (term divided by next term) converges on 0.618 (the Golden Ratio). Get a calculator and fill in the gaps below\n\n5/8 = 0.625\n8/13 =\n13/21 =\n21/34 =\n34/55 =\n55/89 =\n\nAND\n\nThe ratio of successive terms (term divided by previous term) converges to 1.618 = the inverse of the Golden Ratio.\n\n8/5 = 1.6\n13/8 = 1.625\n21/13 =\n34/21 =\n55/34 =\n89/55 =\n\nThe numbers appear in nature eg in the arrangement of leaves on a stalk, sunflower heads, pine cones etc.\n\nThe generating formula, each term is the sum of the last two, can be used to generate other series e.g.\n\n1, 3, 4. 7, 11, 18, 29, 47, 76,\n\nCompare this to\n\n1, 2, 3, 5, 8, 13, 21, 34, 55\n\nand notice how the difference between 55 and 65 is 21, the differemce between 34 and 47 is 13, the difference between 21 and 29 is 8 etc.\n\nThe series starting 1, 4 and 1, 5 and 1, 6  show similar properties\n\n1, 6, 7, 13, 20, 33, 53, 86, 139\n1, 5, 6, 11, 17. 28, 45, 73, 118\n1, 4, 5, 9. 14, 23, 37, 60, 97, \n1, 3, 4. 7, 11, 18, 29, 47, 76,\n1. 2. 3, 5, 8, 13, 21, 34, 55\n\nand they all converge on the golden ratio too.\n\nOne can experiment with other generating formulae\n\neg each term = the sum of the 3 previous terms\n\n0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81\n\nor each term is twice the previous term plus the one prior to that\n\n0, 1, 2, 5, 12, 29, 70, 169\n\nand explore the properties of such series. Have fun!
32358
I don't think anyone recorded it for posterity. It has been mistakenly attributed to Zeno of Elea (circa 490 BC to 430 BC). He has some equally interesting paradoxes:\nhttp://en.wikipedia.org/wiki/Zeno%27s_paradoxes
184734
Actually it does not show the golden ratio, as the first answerer's first referenced web page states: "The nautilus shell spiral is a logarithmic spiral similar to other spirals such as the Golden Mean or phi spiral, but with slightly different proportions." \nYou can tell whether or not it has a golden ratio by measuring some key dimension of a cell that repeats with each cell. See how far apart two cells are which come closest to the golden ratio. If this angular distance seems arbitrary (i.e., not one cell, not one radian, not one revolution, not 1/4 revolution) then the golden mean doesn't apply, but the shell is still approximately based on a logarithmic spiral, a small miracle in itself. \nYou probably also will find that the base of the natural logarithms e isn't exactly shown either. But as an exercise you could use e to find the exponential growth constant K. The nautilus builds a new chamber when the current one beomes too small. This is about every 43 to 77 days (ref.). Thus there is not a per-unit-time constant of growth but rather a per-cell constant.  You count the number of cells N needed for a size ratio = e. Then since e = K^N, K = e^(1/N). Because of changing environmental conditions, each cell will not grow by a constant fraction, but often the differences are too small to be readily perceived. However it might be interesting to measure a few and see how they deviate from a constant value.
216459
2.7182\nLook up Napier's constant (that's what it is called).
29453
This all dates back to the Ancient Babylonians who liked to count in base 60. Ratios of 6, 12, 60, and 360 were seen by them as being 'round' numbers in the same way that we use base 10 and see 5, 10, 100 etc as useful numbers to divide things up into. \n\nSee: http://www-groups.dcs.st-and.ac.uk/~history/ HistTopics/Babylonian_and_Egyptian.html \n\nThe Babylonians divided the sky into the 12 signs of the Zodiac, and a circle into 360 degrees. They divided the day and night each into 12 hours (although in many time systems the lengths of these varied between summer and winter! Babylon was rather nearer the equator than Liverpool, so they didn't get too confused with this). The hour was split into 60 minutes and a minute into 60 seconds. \n\nAll these numbers have survived for 4000 years, despite the fact that we have changed our numbering system to base 10! In England, when I was young, we still measured with feet, each divided into 12 inches. The Americans still do! [By the way, do you know where the mile comes from? It's Roman, not Babylonian!] \n\nThe year is nearly 360 days long and the Babylonians split it into 12 months. Other civilizations based their calendar on the moon and had 13 months. We still have problems with this today because Easter is based on the lunar calendar and migrates around the Julian calendar in a complex way. Chinese new year is still based on the Lunar calendar
38912
well, for me too is the "golden ratio": you can express it as (1+sqrt(5))/2, even if this is not, poetically speaking, it's best definition