Talk:Triangular number

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Mathematics rating:	Start Class	Mid Priority	Field: Number theory
One of the 500 most frequently viewed mathematics articles.
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Currently one long unstructured section consisting of a sequence of unrelated facts. Needs organization and editing. —David Eppstein 01:44, 24 April 2007 (UTC) Add Fermat's Theorem on triangular numbers (first proved by Gauss). I think that a mention of the theorem that every positive integer can be represented as the sum of at most 3 triangular numbers, stated by Fermat and first proved by Gauss in Disquisitiones Arithmeticae, should be added to this page. Perhaps also a reference to its generalization, also stated by Fermat and proved by Cauchy (?) after work by others that every positive integer was a sum of at most 3 triangular numbers, 4 square numbers, 5 pentagonal numbers, etc. Yes I know the history of the 4-square theorem, but I don't think that would be appropriate in the page on triangular numbers. Achava 00:44, 3 May 2007 (UTC)

[edit] Old Comments

Triangular numbers may also be graphically represented by a right angle triangle. Percussim 09:15, 25 April 2007 (UTC)

the part that said n = the floor of sqrt(2x) is misleading at best. if you put for example x=8, you get n=4, but 8 is not the 4th triangular number. i removed it becuase of that.Essap 02:36, 17 May 2007 (UTC)essap

666 is one of the most famous triangular numbers, wherever its fame comes from, and it's known as the "Number of the Beast" first from the Bible, only secondarily from numerology. Many people would have no idea what its numerological significance is, but would know what it meant in the Bible. Jacquerie27

Triangular numbers are presented in "The Ouzo Prophecy," and provide the basis for the construction of the Ouzo Cross.

Robert Merlin Evenson/Church of Ouzo

[edit] Popular Culture

Personally, I wouldn't consider the bible being "pop culture"

bobevenson@yahoo.com

[edit] I have added some links to a video Podcast and they were remove

Hi everyone I have added some links to a video podcast that I own. I think they are a nice addition to wikipedia please look at them and express you oppinion here , judge for yourself if the links are really useful or not to wikipedia.

• [1] Video PodCast by http://www.isallaboutmath.com/

If any of you think they are valuable to wikipedia then feel free to add them back in the external links.

Regards SilentVoice 03:22, 22 January 2007 (UTC)

If your material is sincerely useful, please consider adding to other wikis that are more inclusive, such as wikinfo and wikiknowledge.--69.87.194.231 23:21, 11 February 2007 (UTC)

[edit] Reason for cleanup?

I don't know why this article was tagged for clean up. Having read it a couple of times, the only thing that to me seemed to need cleaning up was the Maple example, which I decided to remove (right decision, wrong decision, I'm not sure). Any reader who has Maple ought to be able to figure out how to use the formulas given here to instruct Maple to calculate these numbers. And if not, he can always look it up in the OEIS. PrimeFan 23:17, 25 February 2007 (UTC)

there are so many theorems and interesting relations between tri#'s and other #'s that it would be difficult to present all of it without the article reading like a long trivia section. i removed that eye-sore table in the introduction.Essap 02:30, 5 May 2007 (UTC)essap

[edit] Formula

I added the simplest formula for finding any given triangle number I could come up with (surprised it wasn't on here) and a little bit of trivia about the formula. I'll be checking back later (this knowledge is the result of a 14 hour plane ride! I want to make sure it's respected) although I may be under a different IP than this one. --24.245.11.103 12:31, 15 May 2007 (UTC)

It was on there. In the second line. —David Eppstein 15:40, 15 May 2007 (UTC)

Oops, I stopped reading that line after the big E looking thing. Sorry, mate! --134.84.5.63 18:43, 15 May 2007 (UTC)

[edit] Not quite perfect

http://en.wikipedia.org/wiki/Perfect_number should probably be read carefully, 10 isn't a perfect number and yet is a triangular number.

It is good to see that others have found what I found about 10 years ago: a triangle root formula. Once I discovered it, I saw that I could extract the root of any polygonal number in existence. It's the 3D numbers that now have me stumped. I know how to generate the tetrahedral and octahedral numbers but have yet to find a way to extract their roots. Any help here is welcome. :) FYI: I am the moderator for http://forums.delphiforums.com/figurate/start

[edit] Not quite perfect continued

The claim is made in this article that all even perfect numbers are also triangular, but the second (third) perfect number, 28, isn't triangular, as far as I can figure out. am I missing something?

Samois98 04:15, 10 July 2007 (UTC)

28 is the 6th (or thereabouts... short term memory problems) triangular number.66.216.172.3 16:51, 10 July 2007 (UTC)

[edit] "Whenever a triangular number is divisible by 3, one third of it will be a pentagonal number"

not true, for instance 6, 21 --86.143.232.149 12:26, 10 July 2007 (UTC).

[edit] "Triangular numbers ... describe numbers of balls that can be arranged in a triangle."

Can someone elaborate on this in the article? It isn't clear to me why I can't fit a non-triangular number of balls into a triangle, or just what sort of balls-into-triangle sense is meant. 66.216.172.3 16:51, 10 July 2007 (UTC)

Yes, this should be made clearer here. Take a look at the graphic at Figurate number to see what kind of triangles is meant. Cheers, Doctormatt 07:52, 14 July 2007 (UTC)

That's what I (eventually) assumed it meant. I'm not sure what the a simple way to describe that would be, other than maybe linking to Figurate number. Does anyone have a good idea? I'll think about it and see if I come up with anything. 207.103.181.5 16:40, 17 July 2007 (UTC)

Games: Here's an image from bowling illustrating T₄: Ten-pin bowling#Pins. And here's one from pool illustrating T₅: Eight-ball#Equipment. /84.238.113.244 (talk) 21:58, 16 March 2008 (UTC)

[edit] Handshake Problem

The 'handshake problem' is not solved by this formula. It would be, if everyone was to shake their own hand. (MKC)

The correct handshake formula is similar see below:

I have removed the statement --Luca Antonelli (talk) 20:25, 14 February 2008 (UTC)

I shall reintroduce the comment on "handshake problem". It was correct. Above post and formula is wrong. Number of handshakes with n persons is T_{n − 1}. Number of handshakes with n + 1 persons is T_n. /84.238.113.244 (talk) 22:06, 16 March 2008 (UTC)