Science Fair Project Encyclopedia
AxelBoldt removed the statement:
Strictly speaking, every polyhedron is also a polygon as is every polytope, since they all have angles.
with the simple claim:
Polyhedra are not polygons.
Since it is obvious that polyhedron have multiple angles, and hence are polygonal, I'd like to give him a chance to explain why he removed true information.
Simple: because it's not true at all. "Polygon" is almost universally defined as a 2-dimensional figure. I don't know of any mathematics text or course that treats it as a superclass that includes 3-d polyhedra. Terms here should be used as they are commonly used in academia. --Lee Daniel Crocker
Lee, perhaps you would like to suggest what term should be used for the class of objects that have multiple angles, regardless of the dimentionality? Then we could put in a reference to that class of objects in this article. I had never heard the term polytope before I got involved with Wikipedia. Does the concept of the angle between two planes make sense? I, admittedly, have found very little accessible material on these topics. -- BenBaker
Maybe a phrase such as:
Even though strictly speaking, every polyhedron has multiple angles, as does every polytope, they are not considered as polygons as the angles between their faces are not two dimensional. They can be classified as 'technical-term', however.
- "Polytope" is the general term, although it is typically only used to refer to 4-d and higher figures (because the 2- and 3-d figures already have names). It is, nonetheless, proper to refer to polygons and polyhedra as subclasses of polytopes. --LDC
Mathematical terms are not defined etymologically. "Polygon" may mean "many angles" in Greek, but that doesn't mean that anything with many angles is called a polygon in mathematics (and yes, you can have angles between planes). Polygons are two-dimensional figures that enclose an area with straight lines. We could have links to polytopes and polyhedra I suppose. --AxelBoldt
I am not aware of any word in any context that is defined by its etymology. Words mean whatever they are defined to mean, regardless of where they happen to come from. Adding an explicit statement to that effect in this article would be silly, because that's just a case of understanding the nature of the English language and has nothing to do with polygons. This article is about polygons, which are flat. Now, if you want to add some statement to the effect that polygons are the two-dimensional instance of the more general class of polytopes, that's entirely appropriate. --LDC
"Words mean whatever they are defined to mean, regardless of where they happen to come from." -- Indeed. That's the Humpty Dumpty argument! (Through the Looking-Glass)
I'd like to mention the term "n-gon" on this page, since that's the link I followed to get here. Also, the table is somewhat inconsistent: a "Triangle" may be regular or not. A "Square" is regular by definition. The other terms usually are taken to mean the regular form -- in my experience it's more common to see a phrase like "an irregular pentagon" than "a regular pentagon".
- Fixed. --Damian Yerrick
On the dimension issue, it might be fair to mention that a polygon is a 2D polytope, but it's not terribly interesting. The question of a "broken" polygon in higher dimensions -- ie a set of non-planar points joined by a closed, simple path -- is perhaps interesting, but completely breaks the definition of a polytope as a convex hull of point, and there's no longer any notion of area or volume. I suppose then it's merely a path. -- Tarquin
Hi. I added a proposed taxonomy, but it does have problems. There is the problem that under the definitions that I left, a complex polygon may be considered convex. Is this indeed the case? If so, the two versions of convex are surely nevetheless considered distinct, so Simple convex and complex convex are distinct classes, both denoted 'convex'? Or am I just being too hopeful in proposing a tree-based taxonomy?
I would prefer a more simple and complete description of the sum of inner angles in an n-gon. Allthough the one used looks simple, it is based on foreknowledge of the sum of angles in a triangle. I sugest something like the following description(better phrased probably).
(For lack of a better word or expression(i can't seem to find it), i will use the term outer angle for the outside coresponding angle which is 180 - inner angle.)
The sum of the outer angles of an n-gon is a full circle.
The average size of an outer angle is therefore 360/n.
The average size of an inner angle is therefore 180 - (360/n).
The sum of inner angles is therefore n * (180 - (360/n)) <=> 180n - 360 <=> 180 * (n-2).
(exscuse the language, english is not my native tongue). Jan Pedersen 09:19 21 Jul 2003 (UTC)
- I added something along these lines. - Patrick 09:48 21 Jul 2003 (UTC)
- its vertices, listed in order as the area is circulated in counter-clockwise fashion,
Is "circulated" the right verb here? AxelBoldt 21:48, 26 Sep 2003 (UTC)
Mathematicians are notoriously incompetent historians. Gauss NEVER gave a proof of the necessity of the constructibility of the regular n-gon. WANTZEL proved this in 1837. If you read otherwise, it's because mathematicians are sloppy historians. Revolver
Names of Polygons??
- A hectagon has 100 sides.
- A chiliagon has 1000 sides.
- A myriagon has 10,000 sides.
- A "megagon " has 1,000,000 sides.
How about 100,000 sides?? 126.96.36.199 21:53, 1 May 2004 (UTC)
Is it necessary to have "googolgon"? The word is an irregular formation and there is no evidence of its ever having been used.
The table of names of polygons specifies for a nine-sided polygon the name "enneagon" and then admonishes "(avoid 'nonagon')".
The discussion further down includes the sentence, "But beyond nonagons and decagons, professional mathematicians prefer the aforementioned numeral notation."
Personally, I think "nonagon" is in sufficiently widespread use to be acceptable even if inconsistent -- much the same way that "quadrilateral" is more widely accepted than "tetragon". So I'd prefer to see the table changed than the sentence in the discussion.
How do other people feel?
To whoever wrote the above discussion, here are some comments. First, when we sign Wikipedia articles, you don't write a word like "Heath"; you just write ~~~~ . I've studied the history of the talk page and found out that you are not a registered Wikipedian. Second, it already says just above the table that "the triangle and quadrilateral are exceptions", as well as a comment saying "(or tetragon)" meaning that quadrilateral is a more well-known word than tetragon, but that both words are equally proper. Third, the info on ennea vs. nona as the prefix for 9 is already mentioned at the bottom of the Greek numerical prefixes article, saying that "In practice, people often use Latin nona- for 9 instead of Greek ennea-." Georgia guy 21:11, 2 Feb 2005 (UTC)
Thanks for the note on the Wiki etiquette -- I'm not (yet) a registered Wikipedian; still learning my way but trying to be constructive in the process. ~~~~ is a tip I hadn't yet seen.
The point that I was trying to make originally is that the table specifically says to "avoid" the word nonagon, while further down the same page the article actually uses that word. The Greek numerical prefixes article does comment further on this, but someone reading this article for the first time is not likely to have seen that other article (I sure hadn't!), and is likely to find the usage in this article contradictory to its own recommendations.
188.8.131.52 03:39, 8 Feb 2005 (UTC) (Heath)
Names of Polygons
Currently, several Wikipedia articles on polygons between 20 and 100 sides are on Vfd and I want to see if anyone plans on creating a Names of Polygons article that is similar to the Names of large numbers article. Anyone in favor of doing so?? Georgia guy 22:56, 10 Feb 2005 (UTC)
What is the Vfd consensus of the polygon articles put on Vfd about a week ago?? Has it been reached yet?? Georgia guy 20:27, 18 Feb 2005 (UTC)
"Moving around a simple n-gon"
This is only a very small problem but I didn't think I should make the edit myself just in case. When I first read this I thought it was talking about moving the whole polygon around. I quickly realised what it really meant, but thought it should be slightly clarified. Moving around on the edges of a simple n-gon There could also be a link on edges if anyone changes it.
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