The golden ratio is not "some arbitrary mathematical ratio that the human mind imposes over certain objects". It is an irrational number, as is pi, for which only an approximation may be calculated. From http://www.gi.alaska.edu/ScienceForum/ASF7/716.html , "Geometrically, it can be defined as the ratio obtained if a line is divided so that the length of the shorter segment is in the same proportion to that of the longer segment as the length of the longer segment is to the entire line. Mathematically, these ratios are such that the longer segment is 1.618054 times the length of the shorter segment, while the shorter is 0.618054 times the longer." (to 6 decimal places) There are a multitude of other references, but the point is that the ratio is not arbitrary. The ratio is found all through nature as it provides efficiency in the growth of living organisms and systems.
As to saying "well, isn't that pleasing", beauty is still in the eye of the beholder. Even if on average folks find this ratio most pleasing in most circumstances, I'm sure many great exceptions will abound - no doubt because of "breaking the rules". I am not a revolutionary, hell, I can't master the basics. For me, I think I'll try to make the "rules" work first. Then I'll try the weird stuff. Regards, Bob.... -------------------------------------------------------------------- "Beer is proof that God loves us and wants us to be happy!" - Benjamin Franklin From: "frank theriault" <[EMAIL PROTECTED]> > Hi, Keith, > > I agree with both you and Dr. Williams. > > But, (it must be that I'm a Libra - hey aren't the zodiac signs Greek?) let me > play devil's advocate here. > > The Golden Ratio, or whatever one chooses to call it, is indeed some arbitrary > mathematical ratio that the human mind imposes over certain objects, and then > says, "well, isn't that pleasing". > > But isn't that the point? It isn't, I suppose, that it's "found in nature", but > that the human mind will impose ~it's~ structures (for lack of a better term) on > what it finds in the world, and judge certain things to be more satisfying than > others.. > > If that's the way some people want to look at and interpret the world, so be it. > > Personally, I think it's poppycock. And I still think that the prevalence of > rectangular photographic paper is due to the overwhelming dominance of 35mm in the > marketplace over the last 50 years or so. > > But, what do I know? <g> As I said before, it's fun to ponder... > > -frank > > Keith Whaley wrote: > > > Regardless of who said it, or who believes it, I propose the so-called > > Golden Rectangle is more an observational circumstance, hardly any > > formal "rule" promulgated by anyone. > > Absent proof of it being someone's "rule" for the wonderfulness of any > > given composition, that will remain my belief. > > Yes, I've seen all the books and articles that draw lines over the > > master's painings and sketches, thereby "proving" the work was > > purposefully laid down with the Golden Rectangle in mind. > > I contend it's something that if you're really obscessed with, you can > > find that pattern almost anywhere in a good composition... > > Quote any old-time artist's writings that set forth such a plan with > > respect to the generation of his or her composition, and I'll consider > > changing my mind. Until then, I'll simply believe it's an observation, > > overlaid on a pleasing scene. > > > > -- > "The optimist thinks this is the best of all possible worlds. The pessimist fears > it is true." -J. Robert > Oppenheimer > > >
