View Full Version : A 13 sided shape (naming your polygons)

JamesEB

07-27-2007, 07:20 PM

I was thumbing through the archive, and found someone asking for the name of a 13 sided shape (https://academicpursuits.us/classics/a3_252.html) . Though this article is from Sep. 88', 7 months after I was born, I wanted to shed more light.

I saw the "freelance" attempt at naming it and thought to myself. I distinctly remember in Trig, we had a primer chapter at the beginning of the book that said after "do decagon"(sp?), all shapes should be referred to as "n-gon", n simply being the number of sides. Though this may simply be so you don't spend an extra year in school memorizing what a tetracontakaienneagon(49 sides).

The following site as the whole system and the explanation.

http://mathforum.org/dr.math/faq/faq.polygon.names.html

I believe its interchangeable, and that everyone will know what you mean if you say a 21-agon instead of icosikaihenagon or icosihenagon. I see it much like the binomial nomenclature we all learned about in bio. You say thats a Ground Hog, I say its a wood chuck, he says its a marmot, but its really a Marmota monax.

In other words, yes there is a name for all shapes with multiple sides, but who really cares?

(Apparently I do, because that article is almost old enough to drink.)

Liberal

07-27-2007, 07:33 PM

Would a polygon with zero sides be a circle?

Yllaria

07-27-2007, 08:06 PM

No - a circle has one side. . . . or an infinite number, depending on how you want to look at it.

Indistinguishable

07-27-2007, 11:47 PM

An interesting point, not mentioned in the article apparently, is that the Susan B. Anthony dollar isn't even decorated as 13-sided. It's decorated as 11-sided.

As for the notion of an n-gon when n is an unorthodox value, there are various ways we could formalize our concept of what an n-gon is for orthodox values, from which to extrapolate, but one natural way, it seems to me, is as the following: an n-gon is a figure which can be described by a cyclic list of n vertices, the figure containing all and only those points which are on line segments connecting adjacent vertices of that cyclic list. With this definition in mind, a 0-gon becomes nothing at all (contains no vertices and no edges), a 1-gon becomes a single point (contains 1 vertex and 1 trivial edge of length 0), and a 2-gon becomes a line segment (contains 2 vertices and 2 (coincidental) edges). That seems mostly right by my intuition, but yours may vary.

Indistinguishable

07-27-2007, 11:57 PM

Also, while a circle is indeed the limiting case of a regular n-gon as n gets arbitrarily large, in a context where regularity doesn't matter, there's nothing unique about the circle in its meriting a claim to the position of infinity-gon. Any closed loop can be made to be the limit of a series of n-gons with n approaching infinity. Draw whatever figure you like on paper without lifting your pen, and as long as you return in the end to the point where you started, you've drawn something with as much claim to being an infinity-gon as a circle, it seems to me.

Telemark

07-28-2007, 12:15 AM

An interesting point, not mentioned in the article apparently, is that the Susan B. Anthony dollar isn't even decorated as 13-sided. It's decorated as 11-sided.

Plus the top and bottom make 13. We're talking about solids, not 2-dimensional shapes.

Indistinguishable

07-28-2007, 12:19 AM

Plus the top and bottom make 13. We're talking about solids, not 2-dimensional shapes.

Ah, that explains it. My misunderstanding, then.

Terrifel

07-28-2007, 11:40 AM

Would a polygon with zero sides be a circle?I think a polygon with zero sides would just be -gon.

Malacandra

07-28-2007, 12:58 PM

I think a polygon with zero sides would just be -gon.

*applauds*

Liberal

07-28-2007, 02:35 PM

*tosses roses*

Yllaria

07-28-2007, 08:21 PM

I think a polygon with zero sides would just be -gon.

Slow clap.

sinjin

08-06-2007, 02:49 AM

If you're talking about dimensions higher than two, "face" is more common in mathematical circles than "side". So a cube has six faces, all of which are squares and a 4-cube (also known as a hpercube or a tesseract) is a four dimensional object which has 8 faces, each of which is a three dimensional cube.

Also, a "three dimensional polygon" is a polyhedron. You can talk about n-dimensional polyhedra if you want to, but they're a bit tricky to draw pictures of.

So a Susie B isn't any type of polygon, it's a polyhedron with thirteen faces. A triskaidekahedron, if you will. Well, it would be one of those if, as Stephanie F. pointed out, it wasn't really just a cylinder.

Also, Indistinguishable, if you want a digon (aka 2-gon) that isn't degenerate, all you have to do is start drawing on the surface of a sphere. Start at the North Pole and walk southwards until you get to the South Pole. Turn left and go back to where you started. Instant digon. Another example is the region which is in both the Northern and Western hemispheres.

Triskadecamus

08-06-2007, 06:41 PM

But, who wouldn't already know that?

Indistinguishable

08-07-2007, 11:23 PM

Also, Indistinguishable, if you want a digon (aka 2-gon) that isn't degenerate, all you have to do is start drawing on the surface of a sphere. Start at the North Pole and walk southwards until you get to the South Pole. Turn left and go back to where you started. Instant digon. Another example is the region which is in both the Northern and Western hemispheres.

Ah, nifty. And even with non-antipodal points, I suppose we could also choose, depending on how we extrapolate the notions involved, to consider the great circle connecting them to be a non-degenerate digon, composed of two distinct sides between its vertices.

Come up with a natural nontrivial interpretation of a 1-gon, though, and I'll be really impressed.

Mangetout

08-08-2007, 05:09 AM

Come up with a natural nontrivial interpretation of a 1-gon, though, and I'll be really impressed.

Start at the north pole and keep walking south until you come to the south pole, carry on straight ahead (now going north) until you return to the place you started. A single line, no corners/angles = 1-gon, or have I missed something important?

Indistinguishable

08-08-2007, 07:59 PM

Start at the north pole and keep walking south until you come to the south pole, carry on straight ahead (now going north) until you return to the place you started. A single line, no corners/angles = 1-gon, or have I missed something important?

Oh, yeah, you've got me there. I suppose I should have been more specific about what was trivial.

Alright, hot shots. 0-gon's the real challenge.

Mangetout

08-08-2007, 08:09 PM

Start at the north pole, then stay there.

Indistinguishable

08-08-2007, 08:32 PM

Start at the north pole, then stay there.

That strikes me as a 1-gon, as much in the spherical case as in the Euclidean case, in the way I described before (1 vertex and one trivial, 0-length edge). But I suppose a case could be made for it as a 0-gon as well; it does, after all, have 0 edges. So, I'll tell you what. I'll give it to you and keep this pattern going.

-1-gon, for the ultimate in unorthodox polygonal excellence. :)

Mangetout

08-09-2007, 03:13 AM

I think you might have beaten me there, although could a -1gon could be formed by some kind of exotic intersection?

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