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Golden Ratio

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    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!
  2. Offline

    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?!
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    Click image for larger version. 

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    Sorry here is the picture!
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    I don't know much about this method, but maybe this PDF will help:
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    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

    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


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