Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathslover

How can we say that in golden ratio : \(\frac{a+b}{a} = \frac{a}{b} \) ??

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    Is their any proof for ^ the above equation?

    • one year ago
  2. amistre64
    Best Response
    You've already chosen the best response.
    Medals 3

    that is simply how it is defined.

    • one year ago
  3. amistre64
    Best Response
    You've already chosen the best response.
    Medals 3

    you might as well ask; is there any proof that green is green

    • one year ago
  4. mathslover
    Best Response
    You've already chosen the best response.
    Medals 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
  5. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry , I meant that : green = green is OK but a/b + 1 = b/a seems hard to agree.

    • one year ago
  6. mathslover
    Best Response
    You've already chosen the best response.
    Medals 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
  7. amistre64
    Best Response
    You've already chosen the best response.
    Medals 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 (1-x)|dw:1350393541608:dw|the golden ratio is defined as the value such that the ratio\[\frac{1}{x}=\frac{x}{1-x}\]

    • one year ago
  8. amistre64
    Best Response
    You've already chosen the best response.
    Medals 3

    by redefining the parts as x = a x-1 = b 1 = a+b we have your setup

    • one year ago
  9. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    sir, but what is the proof that : 1-x = x^2 ? Are we estimating this?

    • one year ago
  10. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    Estimation (in the following sense) : In this special case of golden ratio : (a+b)/b = a/b

    • one year ago
  11. amistre64
    Best Response
    You've already chosen the best response.
    Medals 3

    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

    • one year ago
  12. mathslover
    Best Response
    You've already chosen the best response.
    Medals 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
  13. amistre64
    Best Response
    You've already chosen the best response.
    Medals 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
  14. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    OK thanks a lot sir!

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.