What is exactly golden ratio?

- mathslover

What is exactly golden ratio?

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- Colcaps

you want explaining or you wanna know what it is?

- mathslover

I wanna know what it is.

- anonymous

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## More answers

- 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

http://en.wikipedia.org/wiki/Golden_ratio

- anonymous

Greeks, pops up all over the place....

- Colcaps

yeah diagrams and dimensions use golden ratio

- UnkleRhaukus

golden ratio was not invented, it was discovered

- 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

Michael Maestlin

- Colcaps

or Ancient Greeks

- anonymous

"golden ratio was not invented, it was discovered"
Debatable.

- UnkleRhaukus

it can be measured @estudier

- mathslover

I am making a project on it!

- anonymous

1+1/1+/1+/1+/1...... = GR

- UnkleRhaukus

the limit of the ratio of consecutive fibonacci numbers

- anonymous

Convergents of 1+1/1+/1+/1+/1......are ratios of successive F numbers

- mathslover

sorry to say but : NOT getting it.

- mathslover

\[\color{blue}{\large{\phi}}=\color{red}{\LARGE{GR}}\]?is it so ?

- 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

Notice that the Greeks messed about with this without worrying about the radical (they worried only about the ratio)

- calculusfunctions

@mathslover do you understand?

- mathslover

Understood! Thanks a lot!

- calculusfunctions

@mathslover You welcome. I thought you didn't like my explanation. lol

- mathslover

Not exactly like your thought, but I think it will take time for me to completely understand it!

- 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

@mathslover is this something you're learning in school right now?

- 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

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

http://www.youtube.com/watch?v=5zosU6XTgSY
^ is khanacademy video good for understanding golden ratio further?

- ganeshie8

also watch parthenon reconstruction project video, you may google...

- calculusfunctions

@mathslover I've never checked those videos out. Perhaps I will when I have time.

- 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

lol I never checked that, may be interesting!

- ganeshie8

ideal human form.. in anatomy they use that i think

- anonymous

http://www.vali.de/archives/1117

- mathslover

^ interesting

- calculusfunctions

@estudier that's a wonderful recommendation. Thanks! It is true that the golden ratio can be observed in nature.

- 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

http://www.khanacademy.org/math/vi-hart/v/doodling-in-math--spirals--fibonacci--and-being-a-plant--1-of-3

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