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Golden Ratio

I'm doing an EPQ on number patterns and mathematical constants found in nature and exploited in engineering and our mathematical reasoning.

I have come across golden ratio/golden number which I'm sure many of you know about. However I have found something called "Golden section search" or "Golden section method" I was wondering if anyone knows about it or understands it whether they could explain it by dumbing it down. Any help would be valuable.

I have attached a picture that is used to explain this method, in the image is C to A, as A is to A+B?! I guessing that is the Gold ratio within the method...

Thanks for any help!
Reply 1
Avatar for Amy-Chod
Amy-Chod
OP
Is it a form of something like iterative Formulae, interval bisection & linear interpolation where instead of finding a root you are finding the minimum in an unimodal function?!
Reply 2
Avatar for Amy-Chod
Amy-Chod
OP
GoldenSectionSearch.png

Sorry here is the picture!
I don't know much about this method, but maybe this PDF will help: http://www.google.co.uk/url?sa=t&rct=j&q=golden%20section%20algorithm&source=web&cd=2&ved=0CG4QFjAB&url=http%3A%2F%2Fwww.math.uic.edu%2F~jan%2Fmcs471%2FLec9%2Fgss.pdf&ei=KZoZUOfANITE0QXnwoHoCA&usg=AFQjCNFVnUc0R6i4IHXl7xTae7PpkTY_qQ&sig2=2RI-yrnNNL9wHrYyyWmDKw
Reply 4
Avatar for SubAtomic
SubAtomic
11
Not quite sure what you are saying. But yes C is to A what A is to B if that is what you mean?

Do you have the full details? A proportional divider shows a relationship within that picture.

Will try put it in words but definitely get a second opinion.

A is proportional to A+C and A+C is proportional to A+B.

The smaller of the two vectors? is 0.618 of the bigger vector. If you measure the small vector then the big vector will be 1.618 of the smaller vector.

A = 1.618C , B = 1.618A. A+C = 0.618(A+B) , A = 0.618(A+C).

Sorry, I tried but I don't know if you will get me on this:redface:

A is approx 4.2

B is approx 7

C is approx 2.7

Do the calculations and it may be clearer.

Not even that sure myself:rolleyes: but my calculations show the relationships to be true.

Like 7.0686 * 0.618 = 4.3683.. = A
(edited 11 years ago)

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