mathslover
  • mathslover
What is exactly golden ratio?
Mathematics
chestercat
  • chestercat
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Colcaps
  • Colcaps
you want explaining or you wanna know what it is?
mathslover
  • mathslover
I wanna know what it is.
anonymous
  • anonymous
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mathslover
  • mathslover
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?
Colcaps
  • Colcaps
http://en.wikipedia.org/wiki/Golden_ratio
anonymous
  • anonymous
Greeks, pops up all over the place....
Colcaps
  • Colcaps
yeah diagrams and dimensions use golden ratio
UnkleRhaukus
  • UnkleRhaukus
golden ratio was not invented, it was discovered
mathslover
  • mathslover
I have to make a chart and a file for it, so what exactly should I write there ? lol, @UnkleRhaukus sorry, Who discovered it? :)
Colcaps
  • Colcaps
Michael Maestlin
Colcaps
  • Colcaps
or Ancient Greeks
anonymous
  • anonymous
"golden ratio was not invented, it was discovered" Debatable.
UnkleRhaukus
  • UnkleRhaukus
it can be measured @estudier
mathslover
  • mathslover
I am making a project on it!
anonymous
  • anonymous
1+1/1+/1+/1+/1...... = GR
UnkleRhaukus
  • UnkleRhaukus
the limit of the ratio of consecutive fibonacci numbers
anonymous
  • anonymous
Convergents of 1+1/1+/1+/1+/1......are ratios of successive F numbers
mathslover
  • mathslover
sorry to say but : NOT getting it.
mathslover
  • mathslover
\[\color{blue}{\large{\phi}}=\color{red}{\LARGE{GR}}\]?is it so ?
calculusfunctions
  • calculusfunctions
@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.
anonymous
  • anonymous
Notice that the Greeks messed about with this without worrying about the radical (they worried only about the ratio)
calculusfunctions
  • calculusfunctions
@mathslover do you understand?
mathslover
  • mathslover
Understood! Thanks a lot!
calculusfunctions
  • calculusfunctions
@mathslover You welcome. I thought you didn't like my explanation. lol
mathslover
  • mathslover
Not exactly like your thought, but I think it will take time for me to completely understand it!
calculusfunctions
  • calculusfunctions
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.
calculusfunctions
  • calculusfunctions
@mathslover is this something you're learning in school right now?
mathslover
  • mathslover
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!
mathslover
  • mathslover
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!
mathslover
  • mathslover
http://www.youtube.com/watch?v=5zosU6XTgSY ^ is khanacademy video good for understanding golden ratio further?
ganeshie8
  • ganeshie8
also watch parthenon reconstruction project video, you may google...
calculusfunctions
  • calculusfunctions
@mathslover I've never checked those videos out. Perhaps I will when I have time.
cwrw238
  • cwrw238
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...
mathslover
  • mathslover
lol I never checked that, may be interesting!
ganeshie8
  • ganeshie8
ideal human form.. in anatomy they use that i think
anonymous
  • anonymous
http://www.vali.de/archives/1117
mathslover
  • mathslover
^ interesting
calculusfunctions
  • calculusfunctions
@estudier that's a wonderful recommendation. Thanks! It is true that the golden ratio can be observed in nature.
anonymous
  • anonymous
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.
anonymous
  • anonymous
http://www.khanacademy.org/math/vi-hart/v/doodling-in-math--spirals--fibonacci--and-being-a-plant--1-of-3

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