## mathslover 2 years ago What is exactly golden ratio?

1. Colcaps

you want explaining or you wanna know what it is?

2. mathslover

I wanna know what it is.

3. estudier

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4. 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?

5. Colcaps
6. estudier

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

7. Colcaps

yeah diagrams and dimensions use golden ratio

8. UnkleRhaukus

golden ratio was not invented, it was discovered

9. 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? :)

10. Colcaps

Michael Maestlin

11. Colcaps

or Ancient Greeks

12. estudier

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

13. UnkleRhaukus

it can be measured @estudier

14. mathslover

I am making a project on it!

15. estudier

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

16. UnkleRhaukus

the limit of the ratio of consecutive fibonacci numbers

17. estudier

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

18. mathslover

sorry to say but : NOT getting it.

19. mathslover

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

20. 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.

21. estudier

22. calculusfunctions

@mathslover do you understand?

23. mathslover

Understood! Thanks a lot!

24. calculusfunctions

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

25. mathslover

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

26. 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.

27. calculusfunctions

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

28. 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!

29. 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!

30. mathslover

31. ganeshie8

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

32. calculusfunctions

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

33. 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...

34. mathslover

lol I never checked that, may be interesting!

35. ganeshie8

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

36. estudier
37. mathslover

^ interesting

38. calculusfunctions

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

39. lharrell97

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.

40. Ishaan94