Talk:Incenter–excenter lemma

move

I undid the move as no source with the supposedly more commmon name was provided and back when the article was created no (common) name was known to the involved authors (or given in the sources iirc).--Kmhkmh (talk) 11:38, 17 June 2023 (UTC)[reply]

There doesn't seem to be a common name for this in English. I would prefer "incenter–excenter lemma" (used by Chen and a few others since) to "trillium theorem" because the former is more descriptive. The names "trident lemma" and "trillium theorem" both come from Russian and neither seems to be in common use in English – the only sources I can find using these names are by Russian authors. –jacobolus (t) 15:52, 21 June 2023 (UTC)[reply]

To be honest I'm not sure if this article would stand up to a notability challenge. Perhaps it should be merged as a section of Incircle and excircles. –jacobolus (t) 15:56, 21 June 2023 (UTC)[reply]

There is reason, why lead back then settled for this maybe slightly awkward and less compact version (exactly because no common name seemed to exist inEnglish back then). Creating "good" names for something not having a name in English literature (yet) is policy violation of sorts as WP/WP authors should not create/define new names/terms but just use names/terms already existing in literature (note the Russian sources use theorem not lemma). You cannot use a foreign language source as a source for an English name/term unless that foreign languahe source actually uses an English term itself. If no English term exist yet, then normally the foreign language term has to be used (or at best in some cases a literal translation of it).

Now if newer sources use a different name or have established an English name for it, then article can be moved to that new name. However in that case a source for than (new) English name should be provided and I can't find Chen(?) under the current sources.

As far as the notability is concerned, back when the article was showed up, several math editors (including myself) looked at it and decided back then it is worth keeping/notable enough based on the Russian sources.--Kmhkmh (talk) 03:37, 22 June 2023 (UTC)[reply]

P.S.: I found Chen now (assuming it was referring to Evan Chen's book on the math olympiad problems) and added it to the article.--Kmhkmh (talk) 10:00, 22 June 2023 (UTC)[reply]

In my opinion the lead should say something like:

In geometry, the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters, is the diameter of a circle also passing through two triangle vertices with its center on the circumcircle. This theorem is best known in Russia, where it is called the trillium theorem (теорема трилистника) or trident lemma (лемма о трезубце). These names have sometimes been adopted by Russian authors writing in English.

These relationships arise because the incenter and excenters of any triangle form an orthocentric system whose nine-point circle is the circumcircle of the original triangle. The lemma is helpful for solving competitive Euclidean geometry problems, and can be used to reconstruct a triangle starting from one vertex, the incenter, and the circumcenter.

–jacobolus (t) 14:39, 22 June 2023 (UTC)[reply]

Update: I applied this proposed language, and added several more references. –jacobolus (t) 19:36, 22 June 2023 (UTC)[reply]

Do you have any Russian sources about 'теорема трилистника' or 'лемма о трезубце' from peer-reviewed or published sources? Are there any Russian speakers here with insights into the origin of the trillium and/or trident names? The links there so far look to me like self-published PDFs, but I don't read Russian. –jacobolus (t) 16:03, 22 June 2023 (UTC)[reply]

Fine with me but please keep the new source(s) for the English name in the lead. In fact now (contrary to 2016) that proper English sources exist, the Russian sources actually might be dropped completely.

The Russian sources in the article are the only ones I'm aware of. I don't speak any Russian, back in 2016 they were provided/researched by User:Stannic, who however doesn't seem to active anymore. --Kmhkmh (talk) 20:08, 22 June 2023 (UTC)[reply]

I'd love to have links to Russian textbooks, published monographs, or journal papers. All the sources I can easily find as a non-Russian speaker (I didn't look especially hard though) are self-published PDFs (arxiv or elsewhere), forum posts, and the like.

Overall it seems like this theorem has been known for a long time (see Johnson 1929, and probably since the 19th century), but doesn't seem to have a well established name outside the Russian problem solving community. Trillium / trident is a more evocative image, but "incenter–excenter" seems more descriptive for readers who have never heard of this before. –jacobolus (t) 20:27, 22 June 2023 (UTC)[reply]

Since we have now an English source with that name in the article, I see no problem with that anymore. As far as the Russian sources are concerned since Stannic is probably not available anymore, maybe you can ask another russian speaking math editor, there should be some around still at the Wikiproject Mathematics.--Kmhkmh (talk) 23:21, 22 June 2023 (UTC)[reply]