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What is exactly golden ratio?

Mathematics
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you want explaining or you wanna know what it is?
I wanna know what it is.
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Other answers:

Why is it known as golden ratio? What is "exactly golden ratio? What are its applications in everyday life, and other things? Who invented it?
http://en.wikipedia.org/wiki/Golden_ratio
Greeks, pops up all over the place....
yeah diagrams and dimensions use golden ratio
golden ratio was not invented, it was discovered
I have to make a chart and a file for it, so what exactly should I write there ? lol, @UnkleRhaukus sorry, Who discovered it? :)
Michael Maestlin
or Ancient Greeks
"golden ratio was not invented, it was discovered" Debatable.
it can be measured @estudier
I am making a project on it!
1+1/1+/1+/1+/1...... = GR
the limit of the ratio of consecutive fibonacci numbers
Convergents of 1+1/1+/1+/1+/1......are ratios of successive F numbers
sorry to say but : NOT getting it.
\[\color{blue}{\large{\phi}}=\color{red}{\LARGE{GR}}\]?is it so ?
@mathslover A line segment which is divided into two segments, with a greater length α and a smaller length β such that the length of α + β is to α as α is to β, is divided into the golden ratio. Hence\[\frac{ \alpha +\beta }{ \alpha }=\frac{ \alpha }{ }\]and\[(\frac{ \alpha }{ \beta })^{2}-\frac{ \alpha }{ \beta }-1=0\]where the positive solution for\[\frac{ \alpha }{ \beta }=\frac{ \sqrt{5}+1 }{ 2 }=\frac{ 2 }{ \sqrt{5}-1 }\]FYI It is also called the golden section or the divine section.
Notice that the Greeks messed about with this without worrying about the radical (they worried only about the ratio)
@mathslover do you understand?
Understood! Thanks a lot!
@mathslover You welcome. I thought you didn't like my explanation. lol
Not exactly like your thought, but I think it will take time for me to completely understand it!
By the way, I just noticed that in my explanation, there is a β missing in the denominator of the right side of the first equation.
@mathslover is this something you're learning in school right now?
1) That was a small mistake, sir, no problem for that. 2) Actually,NO sir, I am in 9th class and their is no such thing so far as I know at least in school learning upto 12th class. But though, I am told to make a project (file,charts) related to mathematics interesting discovery (any) . I chose, golden ratio as my topic for project as it is applicable, understandable etc, A good topic for project, actually, I think!
Usually there are no such things that I have ever seen in the textbooks but ^those studies of new discoveries are very important! Thanks for helping me out!
http://www.youtube.com/watch?v=5zosU6XTgSY ^ is khanacademy video good for understanding golden ratio further?
also watch parthenon reconstruction project video, you may google...
@mathslover I've never checked those videos out. Perhaps I will when I have time.
one thing i read about the golden ratio was it = height of human / height of his/her navel!! not sure if i believe that - lol! seems a bit bizarre...
lol I never checked that, may be interesting!
ideal human form.. in anatomy they use that i think
http://www.vali.de/archives/1117
^ interesting
@estudier that's a wonderful recommendation. Thanks! It is true that the golden ratio can be observed in nature.
a logarithmic spiral, also known at golden ratio or golden spiral, is a spiral curve that is often found in nature. for example, the little diamond shaped sections on the outside of a pineapple are actually spiraling upwards at a constant angle. another example is the angle of descent of a hawk towards it's prey.
http://www.khanacademy.org/math/vi-hart/v/doodling-in-math--spirals--fibonacci--and-being-a-plant--1-of-3

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