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mathslover
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How can we say that in golden ratio : \(\frac{a+b}{a} = \frac{a}{b} \) ??
 one year ago
 one year ago
mathslover Group Title
How can we say that in golden ratio : \(\frac{a+b}{a} = \frac{a}{b} \) ??
 one year ago
 one year ago

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mathslover Group TitleBest ResponseYou've already chosen the best response.0
Is their any proof for ^ the above equation?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
that is simply how it is defined.
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
you might as well ask; is there any proof that green is green
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
You want to say that : (a+b)/a = a/b > if a > b ^ that is : 1 + b/a = a/b , is universal ?
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Sorry , I meant that : green = green is OK but a/b + 1 = b/a seems hard to agree.
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
usually when we are to prove x = y then it is agreed that YES IT IS LIKE GREEN = GREEN but not exactly, it is like : color of leaf = green (TO PROVE) . I hope you are getting my point sir.
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
take a line of unit length (1); take some part of it and define it as "x"; which leaves us with the rest of it as (1x)dw:1350393541608:dwthe golden ratio is defined as the value such that the ratio\[\frac{1}{x}=\frac{x}{1x}\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
by redefining the parts as x = a x1 = b 1 = a+b we have your setup
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
sir, but what is the proof that : 1x = x^2 ? Are we estimating this?
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Estimation (in the following sense) : In this special case of golden ratio : (a+b)/b = a/b
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
when 1x = x^2 the ratio of the parts to the whole IS the golden ratio. this is along the same line of thought as: the ratio of the circumference of a circle to its diameter defines pi. How would you prove the C/d = pi ? its not a matter of proof, but of definition
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
So can we regard that as , axiom ? postulate? Well I think it can be defined well as 'definition' , correct? btw, a nice example given by you sir.
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.3
id say "definition" is a good term to use :) we can prove that the value of the golden ratio is what it is by solving for "x"
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
OK thanks a lot sir!
 one year ago
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