Talk:hyperbolic geometry

This page has been nominated for deletion. It should be kept. It is an established term and an important concept in mathematics.--Solomonfromfinland (talk) 02:33, 27 December 2020 (UTC)

@Solomonfromfinland You can defend the entry at the discussion here. Ultimateria (talk) 01:33, 28 December 2020 (UTC)

RFD discussion: December 2020–February 2021

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hyperbolic geometry

This seems SOP. There is a lemming. Personally I lean keep. ←₰-→ Lingo ^Bingo _Dingo (talk) 18:26, 24 December 2020 (UTC)

Bolded my keep vote. ←₰-→ Lingo ^Bingo _Dingo (talk) 12:00, 29 December 2020 (UTC)

• It's borderline. As defined, it's very slightly more specific than the sum of parts thanks to the word "constant". Does anybody see an essential difference between the (mathematics) and (topology) senses of hyperbolic? Vox Sciurorum (talk) 19:27, 24 December 2020 (UTC)
• I suspect that the term hyperbolic geometry preceded, and gave rise to, the senses 3 through 5 of Etymology 2 of the adjective. I think the usex at sense 4 of the adjective {{m|en|hyperbolic} actually is an example of use of sense 5, and that the given definition of sense 4 does not make mathematical sense. (Although it is a theorem of geometry that a great circle has the same circumference and centre point as its sphere,^[1] it does not make sense to define great circle as “A curve that has the same circumference and centre point as its sphere.") For a somewhat similar situation, consider the term acrylic acid: the meanings of the adjective acrylic are derived from acrylic acid, in which the adjective that distinguishes it from other acids references its characteristic tart smell. Sense 3 of Etymology 2 can only be applied to geometry (the uncountable noun, a branch of mathematics studying a specific kind of geometries) or to a geometry (a plane, a space, a manifold: mathematical structures studied in hyperbolic geometry). It then determines a defining characteristic of these geometries. Sense 5 can be applied to entities that are not themselves geometries, but that are constructions that play a role in hyperbolic geometry. The label topology can be left out; like all metric spaces, hyperbolic manifolds are topological spaces, but their defining characteristic, negative curvature, is a concept that is alien to topology.  --Lambiam 03:41, 26 December 2020 (UTC)

  On this point, Wiktionary:JIFFY is relevant. ←₰-→ Lingo ^Bingo _Dingo (talk) 12:00, 29 December 2020 (UTC)

• Keep >SOP, lemmings. Anybody who can work out what "hyperbolic geometry" is by taking a minute or so to go through all the senses of "hyperbolic", then another minute or so for "geometry", joins "hyperbolic" + "geometry" and deduces this, is a genius in my book. — Dentonius 11:07, 26 December 2020 (UTC)

• Keep Coming from the same direction of Dentonius; if you can go from hyperbolic + geometry to Lobachevsky's geometry, you already knew what hyperbolic geometry was. I've taken a course in non-Euclidean geometry and couldn't explained which sense of hyperbolic was used and why. From my axiomatic mathematical perspective, I would regard it as the unique geometry that comes from adding the appropriate version of the parallel axiom to absolute geometry. It strikes me like deleting green woodpecker because it's a woodpecker that's green, and so what if there's only one species of green woodpecker and it uniquely identifies that species. (w:green woodpecker disagrees, and offers four species to choose from, but the basic point stands.)--Prosfilaes (talk) 03:43, 27 December 2020 (UTC)
• Comment. We have an "of a geometry" sense at hyperbolic. If this does not correctly explain the meaning of "hyperbolic" in "hyperbolic geometry" then it should, and, when it does, "hyperbolic geometry" will be SoP. Mihia (talk) 15:01, 27 December 2020 (UTC)
  • We have a color sense at green. Does it not correctly explain the meaning of "green" in green woodpecker? Does not jump correctly explain the meaning of jump in jump rope? The only appropriate sense "of a geometry", IMO, would be "pertaining to the geometry of Lobachevsky and Bolyai", or something similar, whereas it would more appropriate to keep "hyperbolic geometry" in its own entry and point certain senses of hyperbolic to it if necessary; that a name is not completely opaque doesn't make it SoP.--Prosfilaes (talk) 05:42, 28 December 2020 (UTC)

    This is more or less the point I was trying to make above. A very proper definition for hyperbolic when used as an attribute of geometry would be: “being a hyperbolic geometry (q.v.)”. The adjective in this sense comes from the noun phrase, not the other way around.  --Lambiam 14:02, 28 December 2020 (UTC)

    OK, well, my comment was predicated on the continuing existence of an "of a geometry" sense at "hyperbolic" other than "hyperbolic geometry = hyperbolic geometry". Mihia (talk) 23:33, 28 December 2020 (UTC)

    @Lambiam, Mihia, Vox Sciurorum, could any of you be enticed to post a bolded vote? ←₰-→ Lingo ^Bingo _Dingo (talk) 12:00, 29 December 2020 (UTC)

    I am reading up on the history of the term to decide where all this hyperbolic stuff started. Independently, I added what I consider the more usual or more elementary sense of hyperbolic geometry. Vox Sciurorum (talk) 14:15, 31 December 2020 (UTC)

• Keep as a mathematical term. There is a Wikipedia article as well as the M-W lemming. DonnanZ (talk) 12:07, 28 December 2020 (UTC)
• Keep, per DonnanZ. --Robbie SWE (talk) 12:24, 28 December 2020 (UTC)
• Keep per Dentonius and Prosfilaes. I doubt most of us (even educated Wiktionarians) could tell the meaning of this without a separate entry for it; I definitely couldn't. Glades12 (talk) 12:42, 28 December 2020 (UTC)
• Keep. This is the name of a type of geometry and therefore a unit. It's not just an adjective-noun pair, nor can its meaning be fully deduced from its meaning (along the lines of fried egg). Andrew Sheedy (talk) 00:00, 29 December 2020 (UTC)
• Keep per the fried egg criterion.  --Lambiam 12:35, 29 December 2020 (UTC)

RFD-kept — surjection ⟨??⟩ 17:29, 8 February 2021 (UTC)