mathslover
  • mathslover
How can we say that in golden ratio : \(\frac{a+b}{a} = \frac{a}{b} \) ??
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathslover
  • mathslover
Is their any proof for ^ the above equation?
amistre64
  • amistre64
that is simply how it is defined.
amistre64
  • amistre64
you might as well ask; is there any proof that green is green

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathslover
  • mathslover
You want to say that : (a+b)/a = a/b --> if a > b ^ that is : 1 + b/a = a/b , is universal ?
mathslover
  • mathslover
Sorry , I meant that : green = green is OK but a/b + 1 = b/a seems hard to agree.
mathslover
  • mathslover
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.
amistre64
  • amistre64
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 (1-x)|dw:1350393541608:dw|the golden ratio is defined as the value such that the ratio\[\frac{1}{x}=\frac{x}{1-x}\]
amistre64
  • amistre64
by redefining the parts as x = a x-1 = b 1 = a+b we have your setup
mathslover
  • mathslover
sir, but what is the proof that : 1-x = x^2 ? Are we estimating this?
mathslover
  • mathslover
Estimation (in the following sense) : In this special case of golden ratio : (a+b)/b = a/b
amistre64
  • amistre64
when 1-x = 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
mathslover
  • mathslover
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.
amistre64
  • amistre64
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"
mathslover
  • mathslover
OK thanks a lot sir!

Looking for something else?

Not the answer you are looking for? Search for more explanations.