Wikipedia:Reference desk/Archives/Mathematics/2007 January 10

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January 10

Latin squares

If all Latin squares can be reduced, does this not mean that every quasigroup is a loop? —The preceding unsigned comment was added by 149.135.97.128 (talk) 11:09, 10 January 2007 (UTC).

Since I was under the impression that loops are quasigroups with identity, no, not every quasigroup is a loop. Whether or not that bit about the Latin squares means the fact you stated, I can't be sure. I don't think any manner of Latin squares can change that. –King Bee ^{(talk • contribs)} 13:32, 10 January 2007 (UTC)

I think I figured it out. The reasoning is this: A Latin square is the multiplication table of a quasigroup. The statement on the article is that the rows and columns of a Latin square can always be permuted so that the leading row and column of the Latin square is naturally ordered. I believe I erroneously thought that this then would imply that the quasigroup has an identity element. However, the ordering of the elements in the table would need to be permuted also, so while it may appear that the quasigroup would have an identity element straight from the table, it would not behave as an identity. —The preceding unsigned comment was added by 149.135.97.128 (talk) 23:43, 10 January 2007 (UTC).

You are correct. –King Bee ^{(T • C)} 00:20, 11 January 2007 (UTC)

About polygon names

Hello. My math class is having troubles with polygon names past an eight sided polygon (which is octagon). Could you give me a list, or show me a place on Wikipedia that has a list of names for polygons?

(Ex. 7-sided = heptagon; 8-sided = octagon; 9-sided = ?)

We're prolly going to flunk math if we don't learn these names. Thanks!!

--NapalmRiot 20:30, 10 January 2007 (UTC)

I doubt anyone would flunk math based only on whether or not they knew these names. Anyway, the 9-gon is called a "nonagon,", the 10-gon is called the "decagon," and so forth. You can check out numerical prefix to see some other ones. To understand the table properly, note that we usually use the Greek prefixes when talking about -gons and -hedra. –King Bee ^{(T • C)} 20:35, 10 January 2007 (UTC)

A 9-gon is also called an enneagon; nonagon is a barbaric admixture of Latin and Greek.  --Lambiam^Talk 00:07, 11 January 2007 (UTC)

As is "quadrilateral," which is why I said usually. (Although I guess "quadrilateral" is all Latin, but why not tetragon?) Who gets to decide these things anyway? A pox on them all! –King Bee ^{(T • C)} 00:16, 11 January 2007 (UTC)

What would the name of a two-sided polygon be, then? Or a three-sided polyhedron? --Carnildo 23:52, 10 January 2007 (UTC)

There is no such thing as a two-sided polygon; they start at three sides. Here is a list of names:

It might be better to say that there is no such thing as a non-degenerate two-sided polygon: there is indeed the concept (as pointed out below) of a Digon, but it doesn't work out with the definitions used for polygons with straight edges and embedded in euclidean planes. Similarily, degenerate polyhedra or even polytopes may well have fewer than expected de facto faces. Michiexile 11:43, 11 January 2007 (UTC)

Note that there are gaps in the numbers; for example, there is no 14-gon here. The names for "3-gon" and "4-gon" come from Latin, the others from Greek if we disregard the abomination "nonagon".  --Lambiam^Talk 00:07, 11 January 2007 (UTC)

As stated above, there is no such thing as a two sided polygon, because polygons are two dimensional you need more then two sides. Similarly, there is no such thing as a three sided polyhedron, because they are three dimensional, you need a fourth point to extrude the plane, so to speak, tetrahedron is the least sided hedron with 4 sides. Vespine 00:13, 11 January 2007 (UTC)

If there's no such thing as a two-sided polygon, then what the heck is the Digon article about? =P —Keenan Pepper 02:27, 11 January 2007 (UTC)

Such limited imagination. Go to the Brazilian town of Macapá, a port in the state of Amapá at the mouth of the Amazon River, and plant a flag to mark a vertex on the Earth, considered a sphere. Why this town? Because it lies exactly on the Equator. Begin to draw the edge of a polygon by heading due East, and continue until the edge meets the original vertex, which it must. We thus have a polygon with one vertex, one edge, one face. (The edge divides the Earth into two hemispheres, "us" and "them". Which is which?) In fact, it is a regular polygon, since all (!) the edges have the same length and all the angles are the same. :-D

Now that we've had fun, here's a serious question. Wikipedia has an article on polygons that lists all the names you need, and a web search for 'polygon names' gives another list; so why did you not use these obvious resources before posting here, as the directions at the top of this page advise? --KSmrq^T 03:50, 11 January 2007 (UTC)

This is an encyclopedia of all the human knowledge. We have articles about dragons and witches, even though those don't exist either. – b_jonas 09:43, 11 January 2007 (UTC)

Not only should the questioner simply have looked for "polygon", he/she should use "probably" correctly on a maths site.81.154.107.5 11:52, 11 January 2007 (UTC)

Alas, thank you for the help with the polygon prefixs. The class was getting frustrated, as we happened to be using the higher-number-sided ones more often. I was just kidding about the flunking part, though.

Again, thank you for the help. --NapalmRiot 22:26, 12 January 2007 (UTC)