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Thread: the golden mean

  1. #1
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    the golden mean

    yeah... hello guys well, i´m new over here... well i will ask you guys to apologise my bad english

    i´ve bean seeing the " da vinci´s code" i think its the right name and i saw something about the golden mean ..
    that really got into my mind so i look around to find something ab about that.. i found this page
    http://www.tu-harburg.de/b/kuehn/lec4.html

    i´ve allready understood some basics information

    if there is someone over there who can help .. i will really like that :d


    thanks
    Abu?!
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  3. #2
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    Post

    i really dont know how this principle could apply to drawing, if its the golden mean i've been thinking about. The only golden mean i saw in the link you provided was a mathematical formula that talked about rectangles :p Isnt the golden mean a rule about visual culture or something like that?

    later,
    GriNGoLoco
    "Nihil est in intellectu quod non prius in sensu" | SB | Portfolio | FJGC (blog) | DA (Profile) | EJERCICIOS DE COLOR
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  4. #3
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    Yup, the golden mean IS a mathmatical equation. The 'perfect' ratio. The greeks used it to build their temples, some artists use it for painting, and amazingly enough it is (as far as I know) the most commonly reaccuring equation in nature.

    IE: The bottom of most people's nose sits on the 'golden mean' of their face. Same with the wrist on the forearm, and several other things I can't recall from my classes.

    One of my drawing teachers was big on the golden mean. He showed us all of this. He also used the Mean to lay out a lot of his compositions.

    Hope that confused you to death!
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    thanks the replay

    i searched about the meaning of the "golden mean".. and it really is only an mathmatical equation . I´ve also read that da vinci noticed that the golden mean is found in the human body... anda that he used to make his painting....and was this treasonthat caught my attention...and i also like maths to

    if some one can explane it better ...
    Abu?!
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  6. #5
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    hey, Hjelm, can you please explain this formula for us? it sounds interesting... For what I found, the golden mean is the following:

    in the 6 perspectives for analyzing any image : the golden mean is one of the six possible ethical perspectives . Heres is the definition (taken from "The Media Through Which We See":

    "Aristotles golden mean refers to finding a middle ground or a compromise between two extreme points of view or actions. Formulated in about the fourth century B.C., this philosophy of taking the middle way doesnt involve a precisely mathematical average but is an action that approximately fits that situation at that time. Compromise and negotiation are actions aimed at finding a link between the opposing viewpoints of two competing interests".

    Other upossible aspects in the ethical perspective are: categorical imperative, utilitarism, hedonism, the golden rule and the veil of ignorance.

    Later,
    GriNGoLoCo
    "Nihil est in intellectu quod non prius in sensu" | SB | Portfolio | FJGC (blog) | DA (Profile) | EJERCICIOS DE COLOR
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    Well I don't know what all that garbeldegook was that YOU found. Doesn't sound like it has anything to do with math though. The Golden Mean is also referred to as the Golden Section. I googled that term and found sites with the right information.

    I'll post more about it soon, but I'm at work and I'm not really supposed to be on here anyway!

    Have a good.
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    Thumbs up

    ok man, thanks for helping out in this doubt...

    later,
    GriNGoLoCo
    "Nihil est in intellectu quod non prius in sensu" | SB | Portfolio | FJGC (blog) | DA (Profile) | EJERCICIOS DE COLOR
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    Okay... here's the shpeal. Had to do a bit of researching.

    The Golden Mean (I will call it this, since I like the term better) is supposed to be the perfect ratio. Shapes build with the GM are supposed to be the most pleaseing to the eye. The ratio itself one of those hairy numbers that goes on forever. This is part of it:

    ±0·61803 39887 ...
    or
    ±1·61803 39887 ...

    I'm no mathemetician, so I prefer to think of the Golden Mean as the following fraction:

    618/1000

    It's not as precise, maybe, but it's close enough for government work.
    So in order to find the Golden Mean on a line, you'd measure the line, multiply your measurement by 618, then divide that number by 1000.

    Ex: I want to find the Mean on a 5" line.
    5x618=3090
    3090÷1000=3.09
    So the golden mean of 5"(or whatever unit) would be 3.09"(units)

    Take the following rectangle:
    the golden mean
    This rectangle is built using the GM. Doesn't look to special at first glance, eh? Now look at the next:
    the golden mean
    Do you follow? Dividing the rectangle's long side at the Golden Mean created on one side, a square of course. On the other side is a rectangle that is preportional to the original rectangle. The ratio for both is roughly 618/1000!

    If you continue dividing these preportional rectangles, you get something like the following:
    the golden mean
    Adding quarter circles inside each square will give you the shape of a nautilus shell.

    The areas lining up with the golden mean are supposed to be the strongest areas of a composition for example, pretend the following is a 6x3 canvas (units don't matter. It could be inches, feet, meters, miles, etc)
    the golden mean
    Now 6x3 doesn't follow the Golden Mean at all, but if you find the ratio on each side of a canvas and intersect the lines, you should be able to find the 'perfect' place to put focal points. (If you invert the GM lines above, bot Horizontally and Vertically, you should be able to find 4 points)

    My instructor also found that using 'secondary Golden Means' (finding the Golden Mean between the edge and the primary GM lines pictured above) was a good way to place secondary focal points.

    Okay so here's how the ratio applies to the human face. I haven't found any good references for bodies, arms, and legs yet, but I will try.

    the golden mean
    Here is the stunning Nicole Kidman with lines running through her face (Yey!) Hopefully you can understand what's going on here. I took a line and divided it at the golden section, then lined the top and bottom up with different landmarks on the face (chin, top of head, nose, and hairline).

    Most faces fit this pretty closely as you can see below:
    the golden mean
    These are the exact same lines. All I did was swap the faces. His eyes/nose/lips line up just about the same—all on a Golden Mean between two other major points.

    Not all faces will line up on on this diagram. Most of your average 'pretty people' should. If you find a picture of someone who looks a little 'off' check them against the Golden Section. Chances are their nose or something doesn't sit on the Golden Mean.

    Ugh! Too much math.
    If you got confused, read it again. If you're still confused after that, ask and it shall be given.

    Toodles
    Robin

    EDIT: fixed a few spelling errors that mighta caused confusion.
    Last edited by Hjelm; June 10th, 2004 at 12:10 AM.
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  10. #9
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    WOW ... great incredible....

    it was the best explanation that i´ve seen

    thanks a lot man

    i really didn´tunderstand the fourth picture very well

    if..just tried touse these propotions.. and they realy fit well

    see ya !
    Abu?!
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  11. #10
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    Woot~! Interesting stuff! Maybe god is a mathematician
    ...+1 exp
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  12. #11
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    That reminds me of the "golden mask" for perfect face proportions based on the golden mean equation. I think I have it somewhere still. Interested ?

    Now as for God being a mathematician... Everything in nature seems to be orchestrated. Look at a pineapple! Or heck even any kind of tree or sprouts out there. I don't pretend to understand all of it, with my head, but with my heart, yes.
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  13. #12
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    Hey peeps if this stuff is interesting to you watch the movie "Pi" by Darren Aronofsky. Good movie and it talks about the golden mean a lot.

    http://www.imdb.com/title/tt0138704/
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  14. #13
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    ...Maybe God's a nerd. J/K

    Anyways... I'll try to re-explain the 'focal point' thing for Abu. This time with real measurements.

    the golden mean
    Here's a blank 'canvas' that's 5x6" large. The canvas itself was not based on the Golden Mean. 5/6 isn't preportional to 618/1000, but you can still use the GM to find what are supposed to be natural 'strong points' on the canvas.

    I took the measurement of each side and found the GM on them. Anything that lays on one of these lines is supposed to naturally draw the eye, and anything that sits on an intersection of the lines is supposed to get even more attention, so if you plan a focal point on an intersection between two GM lines, it's supposed to strengthen your focal point.

    Here's something to clarify what I meant by finding secondary focal point locations:
    the golden mean
    Hopefully that's clear enough. I'm afraid if I try to explain it in words, I'll just make it more confusing.

    Thanks egerie and Groover for pitching in. I don't claim to be an expert on the Golden Mean, so any extra information is helpful!

    I just read an article in a CG magazine about some people creating 'perfect' CG 'actors' for 3D animation. The faces are based on the Fibonacci numbers and the Golden Mean (which is somehow related to the Fibonacci numbers, though I'm not sure how). Actually I thought their 'perfect' faces looked kinda ugly, but that was probably more the fault of the skin than the model.

    Eh whatever.

    Have a good!
    Robin
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