Talk:Kepler triangle

Kepler triangle has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. Review: February 23, 2022. (Reviewed version).

A fact from Kepler triangle appeared on Wikipedia's Main Page in the Did you know column on 13 March 2022 (check views). The text of the entry was as follows: Did you know... that although the Kepler triangle has similar proportions to the Great Pyramid of Giza, the triangle's connection to the golden ratio makes it unlikely to have been used in ancient Egypt? A record of the entry may be seen at Wikipedia:Did you know archive/2022/March. The nomination discussion and review may be seen at Template:Did you know nominations/Kepler triangle.

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the current illustration would mean that traversing two sides of the triangle would require the same distance as traversing its hypotenuse. Alas, if only such a triangle truly existed. I was unable to change this illustration unfortunately. Owen214 (talk) 13:39, 23 August 2010 (UTC)Reply

You've misread both the illustration and the caption, I think: those aren't side lengths, they're areas. —David Eppstein (talk) 16:08, 23 August 2010 (UTC)Reply

That makes the diagram even worse then, there's no indication that those are meant to be squares. Wouldn't it be more useful just to have a diagram with the actual side lengths? Owen214 (talk) 05:35, 25 August 2010 (UTC)Reply

The caption says "A Kepler triangle is a right triangle formed by three squares with areas in geometric progression according to the golden ratio." Or are you looking at something different? Dicklyon (talk) 05:47, 25 August 2010 (UTC)Reply

People naturally focus on the pictures first and may not even read the text. The digram should be complete without having to read the caption. This current diagram doesn't take proper consideration of the encyclopaedia's guests. Even if you want to keep it with areas labelled, the squares are not currently labelled as being squares; none of their sides have markings and neither do their angles. Owen214 (talk) 08:22, 5 November 2010 (UTC) Are you sure that the illustration is only difficult to read, it seems to me that it is also wrong, if the base is 1, i guess that we should read 1, square root of phi and phi, and not 1, phi, and square phi. — Preceding unsigned comment added by 79.9.54.236 (talk) 16:43, 11 June 2015 (UTC)Reply

Who is Marty Stange? And why is it related to the Fibonacci sequence?

This reasoning works with any sequence in which each number is the sum of the previous two, not just Fibonacci, since any random sequence approaches Phi as larger numbers are used in the series.

FJofre (talk) 12:57, 9 August 2021 (UTC)Reply

This review is transcluded from Talk:Kepler triangle/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: NSNW (talk · contribs) 01:07, 23 February 2022 (UTC)Reply

Hello! I will be reviewing this Mathematics Article Feel free to come by on my user page or talk page if you want to ask questions. The process of reviewing this article may take ~7 days more or less. Probably less. This is my first time reviewing an article and I'm not very into mathematics so if you can help me in any way possible please do! I will start reviewing the nomination tomorrow as I have personal issues that I need to deal with. — NSNW 01:07, 23 February 2022 (UTC)Reply

Thanks! Except for one minor point (the reference to Coxeter's circle packing) I hope all the math is at the level of high school geometry, algebra, and trigonometry; I don't think this topic needs anything more advanced than that. —David Eppstein (talk) 02:01, 23 February 2022 (UTC)Reply

GA review (see here for what the criteria are, and here for what they are not)

This is a very well done article, only a few minor things need to be cleaned up.

1. It is reasonably well written.

   a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists):

   Complies with all.

2. It is factually accurate and verifiable.

   a (reference section): b (citations to reliable sources): c (OR): d (copyvio and plagiarism):

   [3] only redirects to a site that requires a license to view the source, it says that those without a license still can access links to them but the site says there are no links to that specific source. This is the first time I've seen a site like this so I may be wrong, but would there be any other way to access this, and if so change to source to make it more accessible?

   I don't think there is, unfortunately. (The same review claims to be available on academia.edu but I suspect it may be a pirated copy, in which case we cannot link to it here, and anyway that site also requires registration to see any content.) I think copying and pasting it here would also be problematic with respect to copyright. Wikipedia does not require sources to be available free online, or even online at all. If you have access to a public university library you may be able to view it from there; my university has a subscription, for instance, valid for all campus internet addresses, so if you signed into the internet using campus guest access from anywhere on campus you would be able to see it. —David Eppstein (talk) 22:15, 23 February 2022 (UTC)Reply

   And after typing all that, and failing to find any other copies through Google, I found it on Hoyrup's personal site: [1]. Will add link to article. —David Eppstein (talk) 22:19, 23 February 2022 (UTC)Reply

   Good Work! As this was really the only issue I had with the article I will pass the nomination. NSNW (talk) 22:30, 23 February 2022 (UTC)Reply

3. It is broad in its coverage.

   a (major aspects): b (focused):

   Very focused on the topic.

4. It follows the neutral point of view policy.

   Fair representation without bias:

5. It is stable.

   No edit wars, etc.:

   No edit wars.

6. It is illustrated by images and other media, where possible and appropriate.

   a (images are tagged and non-free content have non-free use rationales): b (appropriate use with suitable captions):

7. Overall:

   Pass/Fail:

   This article seems to be easily passable if the above issues are resolved, I will put the nomination on hold so that you can fix the issues.

8. Updated Overall:

   Pass or Fail:

   Thanks for fixing the issues and bringing the article up to standard, I will pass the nomination now.

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Rlink2 (talk) 03:25, 6 March 2022 (UTC)Reply

(

• Comment or view
• Article history

)

Isosceles triangle with the largest inscribed circle for its side lengths

To T:DYK/P2

• ... that an isosceles triangle formed from two Kepler triangles (pictured) has the largest inscribed circle of any isosceles triangle with the same two sides? Source: [2] (paywalled)
  • ALT1: ... that when a right triangle's sides are the Pythagorean means, it can only be a Kepler triangle? Source: [3]
  • ALT2: ... that the three sides of a Kepler triangle form a geometric progression whose common ratio is the square root of the golden ratio? Source: Herz-Fischler reference in article (offline)
  • ALT3: ... that although the Kepler triangle has similar proportions to the Great Pyramid of Giza, the triangle's connection to the golden ratio makes it unlikely to have been used in ancient Egypt? Source: The article lists four sources for this claim, of which the only non-paywalled one is Markowsky, Misconceptions about the Golden Ratio ("Misconception: the great pyramid was designed to conform to ${\displaystyle \Phi }$", p. 6; figure depicting the triangle in a pyramid, p. 7; "It does not appear that the Egyptians even knew of the existence of ${\displaystyle \Phi }$ much less incorporated it into their buildings", p. 8)
  • Reviewed: Template:Did you know nominations/Ronen Eldan
  • Comment: Image intended only for ALT0. ALT3 may be the best choice for a wide audience, though, as it is less technical than the others.

Improved to Good Article status by David Eppstein (talk). Self-nominated at 06:22, 25 February 2022 (UTC).Reply

General: Article is new enough and long enough
New enough: Long enough:

Policy: Article is sourced, neutral, and free of copyright problems
Adequate sourcing: Neutral: Free of copyright violations, plagiarism, and close paraphrasing:

Hook eligibility:

• Cited:
• Interesting: - ?

Image: Image is freely licensed, used in the article, and clear at 100px.
Freely licensed: Used in article: Clear at 100px:

QPQ: Done.

Overall: Recent GA article is long enough and sourced. Pic is awesome on all counts. No copyvio, qpq is done. The hooks are cited (AGF on paywalled / offline sources) but I'm not sure how interesting the first three are. ALT3 is the most interesting, but I'm wondering if we can make it a little shorter. Can we just say it's unlikely that the Giza Pyramid is related to the Kepler Triangle, without explaining why (golden ration, etc) in the hook? BuySomeApples (talk) 00:15, 1 March 2022 (UTC)Reply

• Ok, how about: ALT4 ... that the Kepler triangle probably does not match the design of the Great Pyramid of Giza despite its similar proportions? (Note: What I want to say is stronger than merely that this triangle itself was not used: they did not use any other calculation that would have produced the same results as using this triangle. The "probably" is not really intended as waffle, but rather as a concise replacement for something like "this is not something we can know with certainty without a written record of how they actually designed the pyramid but it is the current consensus of scholars that such a design is inconsistent with everything we know about their mathematics and architecture".) —David Eppstein (talk) 00:43, 1 March 2022 (UTC)Reply

• Excellent! Approving ALT3 and ALT4. BuySomeApples (talk) 04:06, 4 March 2022 (UTC)Reply

To say we do not use the basic relations of mathematics is absurd. To think it bears much speech but witness, also fool. — Preceding unsigned comment added by 2001:1C02:C1D:4E00:3012:DADE:352D:9476 (talk) 10:00, 13 March 2022 (UTC)Reply

It always takes me a moments to speech of this level... The proportions of triangle are not fixed as are they to all points, but to the line, yes, but the line only to it's one point, and the three only seperately conjoined, for else the triangle was the fix. The Fix is the place of anchorage within the explorer of the meme-plex or some word to the notion. We do not limit ourselves to any particular dimensionality. — Preceding unsigned comment added by 2001:1C02:C1D:4E00:3012:DADE:352D:9476 (talk) 10:04, 13 March 2022 (UTC)Reply