Talk:Golden ratio

Approximation

I removed the sentence which read:

The golden ratio is irrational and, in a sense, the hardest among irrational numbers to approximate by rational numbers. Only rational numbers are harder to approximate by other rational numbers. Thus one may say that of all irrational numbers the golden ratio is the least irrational.

because it doesn't make much sense to me, and what it seems to be saying appears to me to be clearly wrong. Anthony Argyriou 22:14, 15 October 2008 (UTC)

I don't know if it's right or wrong, but it sure doesn't make any sense to *me*! Please don't think that *I* put it in there! Hayford Peirce 22:45, 15 October 2008 (UTC)

This sentence refers to a fact from Diophatine approximation, but this sentence does not explain. It only makes a mystery out of it. The mathematics section will need reorganization. Peter Schmitt 00:23, 4 October 2009 (UTC)

why does it follow

The article states: "If ${\frac {a}{b}}={\frac {1+{\sqrt {5}}}{2}}$  it follows that ${\frac {a}{b}}={\frac {a+b}{a}}=1+{\frac {b}{a}}$" Why does it follow? I don't follow. --Joe Quick 21:11, 9 September 2009 (UTC)

I hope that's clearer now. --Daniel Mietchen 07:07, 10 September 2009 (UTC)

Yep, that makes more sense. Thanks. --Joe Quick 16:50, 10 September 2009 (UTC)

Hey, ho, people, couldn't we have a Definition that made a *little* sense!?

Has anyone *read* the current definition? What does it have to do with the Golden ratio? Hayford Peirce 06:06, 10 September 2009 (UTC)

Geez, I wuz so aggravated by this dumb definition that I fergot to sign me name?! Hayford Peirce 06:06, 10 September 2009 (UTC)

There is a lot that needs to be done. It would help, right at the beginning if CZ had articles on ratio and proportion...which are not exactly the same thing[1]. (My background is in the visual arts, and it would not be a good idea for me to create those articles.)

In my view the Leipzig old townhall image does very little to explain the subject of the article, but I hesitate to remove it until I can find something better to replace it. Something like this [2] would be more helpful, but I have not yet found a good free use image. (Actually, I would like to add an image gallery showing a number of natural and art works that demonstrate the golden ratio.) I would also like to show some problems with claims made be exponents of the golden ratio, such as claims of the ratio in nautilus shells even though the match is far from perfect [3]. Malcolm Schosha 12:15, 10 September 2009 (UTC)

Silver ratio

Isn't there a silver ratio, too, that is 1.414? D. Matt Innis 15:32, 20 September 2009 (UTC)

Oops, it's 2.414. They all seem to claim that they are pleasing to the eye! D. Matt Innis 19:50, 20 September 2009 (UTC)

Do you mean the \sqrt 2 ? That is 1.414... and is the ratio of the DIN A series. Peter Schmitt 22:32, 20 September 2009 (UTC)

I overlooked the link. But it is of course essentially the same thing (1+). I never heard the name, I have to confess. My guess is that this term was introduced quite recently in a popular or recreational context. Peter Schmitt 22:41, 20 September 2009 (UTC)

Ah, good to know I wasn't going nutz. The number stuck in my head after watching a show about freemasonry and their using the ratio when they built cathedrals, etc, and I then read about both the gold and silver ratios. Unfortunately, all I remembered was that they both existed as architechturally pleasing ratios... D. Matt Innis 00:05, 21 September 2009 (UTC)

It seems to have been the artist and writer Jay Hambridge (there is a short WP article about him, that is not very good) who promoted the use of the root rectangles, and golden rectangle, as proportions in the visual arts, through a series of books he wrote. There was a time I used these proportions, but I no longer bother with it....although for some reason it often turns out to be there even without any intention. The numbers of the proportions (1.616..., 1.414..., etc) are a little meaningless (for artists) divorced from the geometric constructions [4].

I never heard of a "silver proportion", but why not. Malcolm Schosha 14:13, 22 September 2009 (UTC)