Talk:Four vertex theorem

Missing hypothesis

Discrete variations 1-3 presumably require a minimum number of sides, or non-regularity, or something else, but what? --Trɔpʏliʊm • blah 18:11, 5 June 2009 (UTC)

pointy bits

Does an extremum of curvature necessarily imply a cusp on the evolute? —Tamfang (talk) 06:25, 1 December 2019 (UTC)

Dead link correction

There is a dead-link in the references section. I found a working link but am unable to edit the references. I have no idea why.

Here is the correct link https://www.math.ucla.edu/~pak/book.htm for reference number 8 Pak, I. Lectures on Discrete and Polyhedral Geometry — Preceding unsigned comment added by Telugujoshi (talk • contribs) 20:01, 20 May 2020 (UTC)

Problematic statement

The section Definition and examples contains this sentence:

"An ellipse has exactly four vertices: two local maxima of curvature where it is crossed by the major axis of the ellipse, and two local minima of curvature where it is crossed by the minor axis."

But many people consider a circle to be a special case of an ellipse.

Even the linked Wikipedia article Ellipse states that an ellipse is a generalization of a circle.

I hope someone knowledgeable on this subject can fix this.

(No doubt any project as large as Wikipedia must contradict itself, but we should avoid this when possible.) 2601:200:C000:1A0:F4CF:60FC:DCAC:F9C5 (talk) 19:58, 6 June 2022 (UTC)

Given that the very next sentence is about circles, I think we can trust readers not to be deliberately obtuse and to understand that the part about ellipses really means non-circular ellipses. —David Eppstein (talk) 20:20, 6 June 2022 (UTC)

Requested move 12 March 2026

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: moved. Favonian (talk) 11:49, 5 April 2026 (UTC)

---

Four-vertex theorem → Four vertex theorem – Per a recent discussion on Talk:Four color theorem. Our sources use both versions of the title, but more of them avoid the hyphen. And hyphenation is not needed to resolve any ambiguity: parsing the title as four (vertex theorem) does not make sense grammatically nor mathematically. —David Eppstein (talk) 18:39, 12 March 2026 (UTC) — Relisting. Extraordinary Writ (talk) 01:37, 22 March 2026 (UTC) — Relisting. TarnishedPath^talk 09:26, 29 March 2026 (UTC)

• Support per the rationale in the nomination. To echo a remark I made in the earlier discussion, hyphenating would make sense in a case like four-author theorem or four-part theorem, where one is talking about an attribute of the theorem, but here, the theorem itself is not somehow made of four vertices. Stepwise Continuous Dysfunction (talk) 22:30, 12 March 2026 (UTC)
• Oppose per WP:HYPHEN. We generally use hyphens for compound modifiers, which this is the case here. If sources use both, then we should use the one that conforms to our normal formatting rules. Rreagan007 (talk) 17:45, 13 March 2026 (UTC)

  WP:HYPHEN does not say that hyphens are obligatory; it says that There are three main uses. Of the case that is relevant here, it says Hyphens can aid ease of reading (true but not a mandate) and that are particularly useful in long noun phrases (which four vertex is not). It says that A hyphen can help to disambiguate, which as noted above isn't relevant here. It's all good advice, but it doesn't establish a firm rule that we must necessarily follow. Stepwise Continuous Dysfunction (talk) 20:24, 13 March 2026 (UTC)

  It aids in readability here and gets rid of ambiguity, thus a hyphen should be used here. I am not familiar with this subject matter, so "four vortex theorem" could mean that it is the fourth in a series of vortex theorems, which apparently is not the case. The hyphen gets rid of such ambiguity. Rreagan007 (talk) 21:54, 13 March 2026 (UTC)

  The fourth in a series of theorems would be "Fourth vertex theorem" (note vertex not vortex), not "Four vertex theorem". For instance we have Second law of thermodynamics, not Two law of thermodynamics. —David Eppstein (talk) 22:21, 13 March 2026 (UTC)

• Weak support. Hyphens are confusing but to the extent that I understand how they work, this should not be hyphenated because the title is not and cannot be parsed as a compound adjectival phrase modifying "theorem", and there is no disambigutory purpose that it serves. (That said, it's not doing a whole lot of harm.) --JBL (talk) 17:38, 14 March 2026 (UTC)

• Weak support based on more publications avoiding the hyphen. Sesquilinear (talk) 04:10, 22 March 2026 (UTC)
• Weak support per discussion above. Thanks, Glasspalace (talk • contribs) 07:44, 22 March 2026 (UTC)

Note: WikiProject Mathematics has been notified of this discussion. TarnishedPath^talk 09:27, 29 March 2026 (UTC)

• Weak support. I would personally use a hyphen, but think the unhyphenated version is probably more readable. Sławomir Biały (talk) 09:57, 29 March 2026 (UTC)

• Ambivalent. There are many sources using hyphens, while others do not per Google Scholar . Why not write an alternative name in the lede, "four vertex theorem", instead? Dedhert.Jr (talk) 10:14, 29 March 2026 (UTC)

Disagree with adding hyphenation variants in the lede. The hyphenation (or lack thereof) does not seem important enough for recognizing or understanding the topic. —⁠ ⁠BarrelProof (talk) 17:54, 29 March 2026 (UTC)

Agree with BarrelProof—hyphen variants are quite minor and are an extremely common source of variation in English. Calling it out as a bolded alternative name would impede the flow of reading and calling out such a trivial "alternative" would be more obstructive than just proceeding with whichever form is chosen for the article. —Myceteae‍🍄‍🟫 (talk) 01:12, 4 April 2026 (UTC)

• Just a comment:

On the one hand:

«8 Mile Road» has no hyphen, even though «8 Mile» modifies «Road» itself…

On the other hand:

«Three-gap theorem» has a hyphen, even though «Three gap theorem» would be unambiguous & «Three-gap» doesn't modify «theorem» itself…

Likewise:

«Two-body problem», «Two-body problem in general relativity», «Three-body problem», «The Three-Body Problem (novel)», «Euler's three-body problem», «Four-body problem», «n-body problem», & «Many-body problem» have hyphens, even though «n body problem» would be unambiguous & «n-body» doesn't modify «problem» itself…

Likewise:

«Two-body Dirac equations» & «No-win situation» have hyphens, even though…

Personal "conclusion":

Perhaps it's just a matter of clarity (with a hyphen) Vs lightness (without a hyphen)? Then, when in doubt, perhaps hyphenation is preferable on Wikipedia?

(Since I'm not a native speaker of English, I don't vote on such subjects.) —JavBol (talk) 15:04, 3 April 2026 (UTC)

• Support. I agree with the nom's rationale and the other 'support' rationales provided. —Myceteae‍🍄‍🟫 (talk) 01:14, 4 April 2026 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.