Results 1 to 8 of 8

Math Help - Golden Ratio Based from 1..10 ?

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    9

    Golden Ratio Based from 1..10 ?

    My wife and I were having this discussion on the golden ratio being used to measure beauty and thought it would be fun to calculate our own ratings based 1..10 (10 being the perfect golden ratio 1.618)

    We have each of our scores see below:

    first face mesaurment (height / width) = 1.571
    second face mesurment (height / width) = 1.666

    How can we calculate a number based on 10, with 10 being the perfect golden ratio 1.618?

    We tried the followig but it doesn't seem correct:
    first face:
    golden ratio (1.618 - 1.571) = 0.047
    10 - 4.7 = 5.3 ???
    second face:
    golden ratio (1.618 - 1.666) = -0.048
    10 - 4.8 = 5.2 ???

    Thanks,
    -Peter
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778
    Let \varphi be the golden ratio, and let f be a face ratio. Then 0\le|f-\varphi|<\infty. A natural idea is to have a linear function that maps the difference |f-\varphi| to [0, 10] such that the difference 0 is mapped to 10. However, one has to select what value is mapped to 0, i.e., which face ratio is absolutely ugly. For example, one can decide that the ratio 3 is absolutely ugly, so 3-\varphi is mapped into 0. The function that maps [0, 3-\varphi] into [10, 0] is g(x)=10-10x/(3-\varphi), so the measure of beauty for a face ratio f is g(|f-\varphi|)=10-|f-\varphi|/(3-\varphi). Good news: for your values, the measures are both around 9.97; this is because they are very far from the ugliness standard.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    9
    Quote Originally Posted by emakarov View Post
    Let \varphi be the golden ratio, and let f be a face ratio. Then 0\le|f-\varphi|<\infty. A natural idea is to have a linear function that maps the difference |f-\varphi| to [0, 10] such that the difference 0 is mapped to 10. However, one has to select what value is mapped to 0, i.e., which face ratio is absolutely ugly. For example, one can decide that the ratio 3 is absolutely ugly, so 3-\varphi is mapped into 0. The function that maps [0, 3-\varphi] into [10, 0] is g(x)=10-10x/(3-\varphi), so the measure of beauty for a face ratio f is g(|f-\varphi|)=10-|f-\varphi|/(3-\varphi). Good news: for your values, the measures are both around 9.97; this is because they are very far from the ugliness standard.
    I'm a bit rusty with my math but it seems as though the"ugliness" ratio is subjective so would it make more sense to re-write the equation and base it on the perfect golden ration 1.618? If so what would the equation look like? My wife and I are still in disagreement over this.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Pranas's Avatar
    Joined
    Oct 2010
    From
    Europe. Lithuania.
    Posts
    81
    Quote Originally Posted by psmith05 View Post
    I'm a bit rusty with my math but it seems as though the"ugliness" ratio is subjective so would it make more sense to re-write the equation and base it on the perfect golden ration 1.618? If so what would the equation look like? My wife and I are still in disagreement over this.

    Thanks
    I believe the least subjective mapping to the scale [0;10] involves psychiatrists and public surveys...
    Otherwise you can only say difference (or difference in percentage) and be precise about that.

    On the other hand, emakarov provided you with a very thorough example of a simple mapping. If that method satisfies you, my personal advise would be to measure an ugly face ratio and replace number 3 in emakarov's function with your desirable ugly-face-measurement.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778
    it seems as though the"ugliness" ratio is subjective so would it make more sense to re-write the equation and base it on the perfect golden ration 1.618?
    If you want to come up with a grade from 0 to 10, then you need to know what faces earn a 0 (the other end of spectrum is agreed on: golden ratio is worth a 10).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2010
    Posts
    9
    Quote Originally Posted by emakarov View Post
    Let \varphi be the golden ratio, and let f be a face ratio. Then 0\le|f-\varphi|<\infty. A natural idea is to have a linear function that maps the difference |f-\varphi| to [0, 10] such that the difference 0 is mapped to 10. However, one has to select what value is mapped to 0, i.e., which face ratio is absolutely ugly. For example, one can decide that the ratio 3 is absolutely ugly, so 3-\varphi is mapped into 0. The function that maps [0, 3-\varphi] into [10, 0] is g(x)=10-10x/(3-\varphi), so the measure of beauty for a face ratio f is g(|f-\varphi|)=10-|f-\varphi|/(3-\varphi). Good news: for your values, the measures are both around 9.97; this is because they are very far from the ugliness standard.
    Thanks emakarov,

    Like I said both my wife and I are rusty with our math. When I use your formular to solve for g I keep getting 182.36 so obviosuly I'm missing something. I've gone over the equation several times. Here is how I arrived at my answer.

    Using the face ratio of 1.571 I took the absolute value of the difference from the left hand side g(.047)
    After calculaing the right side of the equation I got 9.953/1.382 = 8.571
    To solve for g I divided 8.571/0.47 and got my 182.36

    Any idea where I went wrong?

    Thanks,
    Peter
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member Pranas's Avatar
    Joined
    Oct 2010
    From
    Europe. Lithuania.
    Posts
    81
    Quote Originally Posted by psmith05 View Post
    Thanks emakarov,

    Like I said both my wife and I are rusty with our math. When I use your formular to solve for g I keep getting 182.36 so obviosuly I'm missing something. I've gone over the equation several times. Here is how I arrived at my answer.

    Using the face ratio of 1.571 I took the absolute value of the difference from the left hand side g(.047)
    After calculaing the right side of the equation I got 9.953/1.382 = 8.571
    To solve for g I divided 8.571/0.47 and got my 182.36

    Any idea where I went wrong?

    Thanks,
    Peter
    g(|1.571 - phi|) = g(0.047) = 10 - |1.571 - phi|/(3 - phi) = 10 - 0.047/1.382 = 10 - 0.034008683 = 9.965991317

    Like I said before, you might want to replace (3 - phi) with more realistic (desirable-ugly-face-measurement - phi) in the formula as face ratio of 3 corresponds to face like this (see below) lol
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778
    Using the face ratio of 1.571 I took the absolute value of the difference from the left hand side g(.047)
    After calculaing the right side of the equation I got 9.953/1.382 = 8.571
    To solve for g I divided 8.571/0.47 and got my 182.36
    Here g is not a number. This is how I called a function that maps an interval [1.382, 0] into [0, 10]. So, g(1.382) = g(3 - \varphi) = 0 and g(0) = 10.

    Speaking about this, I realized I made an error. I first wrote that g(x)=10-10x/(3-\varphi), but then said that the final grade is 10-|f-\varphi|/(3-\varphi). Of course, it should be 10-10|f-\varphi|/(3-\varphi), or 10(1-|f-\varphi|/(3-\varphi)). This bumps down your grade from 9.97 to about 9.66.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. About the golden ratio
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 3rd 2011, 02:33 AM
  2. [SOLVED] Golden Ratio
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: June 11th 2011, 06:00 PM
  3. Golden Ratio question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: December 9th 2009, 02:22 AM
  4. Golden ratio
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 17th 2008, 05:15 AM
  5. Golden Ratio equation
    Posted in the Algebra Forum
    Replies: 11
    Last Post: March 24th 2007, 05:12 PM

Search Tags


/mathhelpforum @mathhelpforum