Talk:Triangle

Hatnotes

Four different Unicode characters turn out to be redirects to this page: 🔽, 🔼, 🔺, and 🔻. The total monthly view count for all of these is less than 100. Accordingly, spending hatnote space on them seems like a waste of screen real estate. Redirects are supposed to help with searches, and hatnotes are supposed to help people confused by their searches taking them to the wrong place, but going by the next-to-nothing view counts, nobody is actually getting confused here.

I am also not convinced that "triagonal" is a sufficiently common synonym for space diagonal that it needs to be listed here. It seems to be a niche-within-a-niche term, used by a very small number of recreational mathematics people. The disambiguation notice looks like the only hatnote worth keeping. XOR'easter (talk) 22:41, 1 September 2024 (UTC)

I can't find any examples of "triagonal" meaning diagonal of a polyhedron. I'd dump the hatnote. –jacobolus (t) 00:45, 2 September 2024 (UTC)

As for unicode symbols: these probably should redirect to a page listing the relevant unicode block rather than here to triangle. In general having 🔓 redirect to Lock and key, 👣 redirect to Footprint, 👵 redirect to Old age, 🍕 redirect to Pizza, etc. seems like a misuse of the redirect feature, and likely to be generally unhelpful to readers. It would be better if these all redirected to some page about unicode symbols, japanese telephone emojis, or the like, with links to topics relevant to each picture listed in a table there. –jacobolus (t) 00:50, 2 September 2024 (UTC)

I’ve just added a hatnote for 🔻 and 🔺 unaware that this discussion had taken place. Now, that almost nobody uses the emojis in the search field doesn’t seem like a great argument against having any explanatory hatnotes—if anything, it would be a good reason to delete the redirect altogether. As long as the redirect exists and red triangles are often used with various symbolism, I suggest we either keep the hatnote or change the redirect to point to the disambiguation page Red triangle (listing the different meanings). ~ IvanScrooge98 (talk) 14:31, 29 March 2025 (UTC)

Top 25 report

I'm putting this banner in an ordinary comment. I don't think there's much benefit to putting it at the top of the page and preventing it from being archived. Summary: in the past month Triangle and Eye of providence got about 1.5 million extra views each, weighted toward the first few days, based on their association with a website related to a new Gravity Falls book. During that time this talk page was vandalized a couple dozen times by Gravity Falls fans leaving graffiti, leading to temporary extra editing protection. –jacobolus (t) 03:19, 6 September 2024 (UTC)

Schlafi symbol?

It says that the Schlafi symbol is {3}, but I'm not sure if this should be put here because it specifically says that this is only for equilateral triangles. Thoughts?

VidanaliK (talk) 00:20, 10 December 2025 (UTC)

There is precedent for only putting a Schläfi symbol on regular versions of a triangle on Pentagon. VidanaliK (talk) 00:29, 10 December 2025 (UTC)

@VidanaliK. A Schlafli symbol is a notation for a regular polytopes and tessellation. Since the article talks about triangles in general form, it is not necessarily needed. Dedhert.Jr (talk) 02:00, 10 December 2025 (UTC)

Thanks! VidanaliK (talk) 02:07, 10 December 2025 (UTC)

inconsistency in meaning given for "edges" of a triangle

I think this may just be a typo. In the intro the line segments that make up a triangle are referred to as sides also called edges. But later in the first para. of the Definition, terminology, and types section the article states

and the endpoints or corners are called the edges. 

I think that the word edges should be the word vertices instead. The material in the footnote doesn't call them edges. So, I think the footnoted reference can stand. Its just that one word change is needed. Thanks for considering! Kmk4wiki (talk) 15:01, 19 May 2026 (UTC)

Yeah, a typo. I fixed it. McKay (talk) 05:46, 20 May 2026 (UTC)

Imprecise mathematical definition

The claim that "any three points that do not all lie on the same straight line determine a unique triangle situated within a unique flat plane" is false, unless we require that all of these three points are also the triangle's vertices. There are infinitely many triangles that contain any given set of three points, so in reality six points, not three, uniquely determine a triangle. Similarly, two points only determine a line segment if they're its endpoints. Mnemosyne7384 (talk) 05:51, 27 October 2026 (UTC)

It is obvious to any ordinary reader that "determine a unique triangle" means "are the vertices of a unique triangle". We do not need to phrase this hyperpedantically to avoid motivated confusion by pedants.

(Aside: If you just want triangles passing through points, 6 points is not enough for uniqueness, unless you specify them as 3 pairs which each specify a side.)

–jacobolus (t) 06:08, 27 October 2026 (UTC)

I'm an "ordinary" reader and this was not obvious at all. The word "determine" in geometry always has an associated construction method: for a line or plane, which are infinite objects, that construction method is incidence; for a triangle that's the convex hull under the implicit assumption made by the article or, equivalently, joining the line segments defined by these points as their endpoints.

I don't think that appending a small note like "[... determine a unique triangle ...] of which they are the vertices [...]" to the end of the original phrase is being "hyperpedantic", this makes the construction explicit and unambiguous for encyclopedic and definitional purposes.

And to correct myself: I believe that in fact no finite number of points uniquely determine a triangle without specifying additional restrictions or predicates, so I retract the claim that six points (in general position, of course) determine a triangle. Mnemosyne7384 (talk) 16:20, 29 October 2026 (UTC)

Vertices are already defined in the preceding paragraph, we don't need to redundantly define them again a few lines down. MrOllie (talk) 16:26, 29 October 2026 (UTC)

We don't need to redundantly redefine vertices, just connect the concepts, since the three points aren't any three points, they're three vertices. Mnemosyne7384 (talk) 17:37, 29 October 2026 (UTC)

The word "determine" in geometry always has an associated construction method

In this case the "construction method" is connect the dots. –jacobolus (t) 18:32, 29 October 2026 (UTC)

Exactly. In formal logic, omitting a conjunct changes the truth value of the statement. "Any three non-collinear points determine a unique triangle" read literally asserts existence and uniqueness of a triangle associated with the points under no further constraint, which makes the statement false because infinitely many triangles contain three given non-collinear points without having them as vertices.

The statement is true only under the additional condition "with those points as vertices" or, as you put it yourself, if we "connect the dots". Otherwise, there are multiple ways to associate three points with a triangle other than the vertex assignment, as well as other associations that are equally valid constructions. So this condition is a genuine disambiguation that the bare statement fails to provide. Mnemosyne7384 (talk) 19:05, 29 October 2026 (UTC)

There is no formal definition of "determine", but in this particular case it is trivial to figure out its meaning from context. Our readers are not proof checking robots. –jacobolus (t) 19:18, 29 October 2026 (UTC)