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Cairoun mosque and golden section.
- A 2004 geometrical analysis of earlier research into the Great Mosque of Kairouan reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz. They found ratios close to the golden ratio in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. The authors note, however, that the areas where ratios close to the golden ratio were found are not part of the original construction, and theorize that these elements were added in a reconstruction.
Earlier the our article correctly points out that (almost) all use in architecture and art before the moder era is "false or highly speculative" but then it continues to simply cite Boussora and Mazouz. Their article however false exactly in the "false or highly speculative" category, their analysis is essentially only numerical (and hence questionable) and they do not cite any historical evidence for their claims and the math sources they do cite (Heath, van der Waerden) however are somewhat outdated and essentially considered as "false"/"questionable" from current perspective.
In addition it is at first unclear to me whether the Nexus Journal in which the paer was published can be considered as sufficiently reputable for any claims on the golden ratio.--Kmhkmh (talk) 15:12, 11 April 2013 (UTC)
- That's why it says "according to Boussora and Mazouz." We merely report their analysis; we do not suggest that it is right or important or sensible. Dicklyon (talk) 16:39, 11 April 2013 (UTC)
- Sure, but it begs the question why mentioning it at all and why it would relevant to the article, if it is just another questionable claim by 2 not particularly reputable authors.
- Another problem is that content organization unfortunately suggests somewhat differently. If the article immediately after debunking such approaches and theories describes one of them without further context other than an author attribution, it may suggest to readers that this in an exception to the rule.--Kmhkmh (talk) 18:13, 11 April 2013 (UTC)
The first line... The what-whatofthewhatofthewhat? too many nested of the's. an this to this equals this to that is fine. a this of this of this of this t othis of this, equalls... wtf? 188.8.131.52 (talk) 21:39, 27 June 2013 (UTC)
- I just tried rewriting it with fewer noun phrases. Better? —David Eppstein (talk) 22:50, 27 June 2013 (UTC)
I agree, the first line is incomprehensible even if it is mathematically correct: 'In mathematics and the arts, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to their maximum.' I'd be pretty sure that is NOT how the Greeks defined it, and its hard to see that the Arts would use such an awkward formalism. Much the better explanation is on the page for 'Golden Rectangle' and goes along the lines that a golden rectangle is one such that after a square is removed from it, the remaining portion is also a golden rectangle, and hence has the same aspect ratio (proportions) as the first rectangle. It follows, referring to the figure and considering the whole rectangle (blue and red parts) that the aspect ratio of the sides of the rectangle is (a+b)/a. Similarly the aspect ratio of the remaining portion (red) is a/b. The ability to repeatedly subdivide a golden rectangle means that these two ratios must be equal,thus (a+b)/a = a/b, and this is solved only by a particular value of a/b, which is called phi. John Pons (talk) 09:09, 7 August 2013 (UTC)
Noted that Gandalf61 removed the above insertion on the basis that it was 'too specific' to be included here. I find that surprising given the highly specific nature of the other mathematical content on the page. I think there is a place for descriptive explanations alongside mathematical ones, and feel that Wikipedia is all the poorer when the mathematical perspective dominates. John Pons (talk) 07:56, 8 August 2013 (UTC)
- I said it was too specific to be included in the lead. The lead section of an article is meant to be a brief summary of its contents. If you want to add a description of the properties of the golden rectangle, this should be in the body of the article, not in the lead. Gandalf61 (talk) 08:07, 8 August 2013 (UTC)
Can editors find citations that show how this recurrence relation approximates The Golden Ratio?
It can be shown that xn + 1 = 1 + (1 / xn) converges to The Golden Ratio with x1 = 1 as n → ∞. This is strikingly similar to the expression used to generate the number e. The differences in the two are that the expression used to approximate e is raised to the power of x and that it is not a recurrence relation.184.108.40.206 (talk) 22:05, 19 October 2013 (UTC) — Preceding unsigned comment added by 220.127.116.11 (talk) 22:03, 19 October 2013 (UTC)
- This is just the standard continued fraction for the golden ratio. See the "continued fraction" line in the infobox in the Calculation section. —David Eppstein (talk) 22:39, 19 October 2013 (UTC)
The Golden Ratio can also be expressed as the solution to the quadratic equation x^2 + x - 1 = 0 by completing the square to obtain x = sqrt(1.25) + 1/2 18.104.22.168 (talk) 04:46, 14 November 2013 (UTC)
- that's just another way of solving the quadratic though. As one method is already mentioned we don't need another: the curious or those who prefer completing the square can use that instead.--JohnBlackburnewordsdeeds 04:53, 14 November 2013 (UTC)
"Adding fuel to controversy over the architectural authorship of the Great Pyramid, Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height, except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ."
"the 3:4:5 triangle was the only right triangle known to the [ancient] Egyptians" is unverifiable and illogical. If an individual can create two measured lines (sharing an endpoint) and make them perpendicular to one another, then that person can construct any right triangle.
"they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ." is unverifiable.
- Take it up with Eric Temple Bell's ghost. We are merely reporting what he said. —David Eppstein (talk) 06:05, 15 November 2013 (UTC)
That the Ancient Egyptians did know about irrationals, and that they did base their entire number system and way of doing mathematics on them, as grounding principles is outlined in detail in R A Schwaller de Lubicz's The Temple of Man - 2 Vols - Trans. Lawlor & Lawlor - ISBN 978-0892815708. Your article should take the timeline back far enough to include this information.22.214.171.124 (talk) 21:18, 17 January 2014 (UTC)