Template:Did you know nominations/Kepler triangle

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)
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• ... 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: [1] (paywalled)
  • ALT1: ... that when a right triangleTemplate:'s sides are the Pythagorean means, it can only be a Kepler triangle? Source: [2]
  • 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 $\mathrm{\Phi }$", p. 6; figure depicting the triangle in a pyramid, p. 7; "It does not appear that the Egyptians even knew of the existence of $\mathrm{\Phi }$ 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).

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• 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)

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

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