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May 7

Simple geometric construction for the metallic ratios

So my previous question has lead me to yet another interesting "discovery". Consider a right triangle with side lengths 1 and N/2, respectively. It turns out that the sum of the hypotenuse and the second side will be equal to the Nth metallic ratio. Now I'd love to include this fact in the article. Only problem I've found zero references thus far. Has anyone else seen this anywhere? Earl of Arundel (talk) 08:09, 7 May 2021 (UTC)[reply]

It is mentioned (in a form that is slightly different but essentially equivalent) in this paper, in the section "A Right Angled Triangle for each Metallic Mean" on page 32. The observation hardly represents an "advance in mathematics"; I'd classify it as being, rather, at the level of elementary "recreational" mathematics. --Lambiam 09:29, 7 May 2021 (UTC)[reply]

Thanks! And yes I agree, hardly earth-shattering stuff. I only recommended adding it to the article because it seemed like such an intuitive result.

Earl of Arundel (talk) 10:13, 7 May 2021 (UTC)[reply]

Also here. (Doi.org does not find the given DOI in the DOI System.) The author is one of the editors of the journal, so this has a tinge of being self-published. --Lambiam 10:51, 7 May 2021 (UTC)[reply]

Not sure about that one. That looks more like a generalized notion of kepler triangles or somesuch.

Earl of Arundel (talk) 13:53, 7 May 2021 (UTC)[reply]