Monogon
Leroy Quet
rather than the mathematical side.
A polygon with 4 sides: quadrilateral
A polygon with 3 sides: triangle
With 2 sides: line segment? (twice drawn)
With 1 side (but closed, as polygons of 3 or more sides): ???????
Of course, such a polygon does not exist in the REAL world.
But what about in an abstract sense?
Of course, of course....
What would it be called? A monogon? A monoangle?
It wouldn't be a line segment (as the bigon/biangle), because a line
segment has 2 vertexes, its endpoints.
Calling a line segment a bigon/biangle is a stretch itself, though I
might have seen this before.
And, last question, if a monogon/monoangle is simply a point, how is
this to be distinguished from a 0-sided polygon?
Hmmm....
(All in fun...)
Thanks,
Leroy Quet
Leroy Quet
Leroy Quet
rather than the mathematical side.
A polygon with 4 sides: quadrilateral
A polygon with 3 sides: triangle
With 2 sides: line segment? (twice drawn)
With 1 side (but closed, as polygons of 3 or more sides): ???????
Of course, such a polygon does not exist in the REAL world.
But what about in an abstract sense?
Of course, of course....
What would it be called? A monogon? A monoangle?
It wouldn't be a line segment (as the bigon/biangle), because a line
segment has 2 vertexes, its endpoints.
Calling a line segment a bigon/biangle is a stretch in itself, though I
Bjorn890
>
>With 2 sides: line segment? (twice drawn)
>
>With 1 side (but closed, as polygons of 3 or more sides): ???????
A a figure with two sides is and undefied angle.
BJORN890
David W. Cantrell
> This question has been inspired more by the poetic half of my brain,
> rather than the mathematical side.
>
> A polygon with 4 sides: quadrilateral
>
> A polygon with 3 sides: triangle
>
> With 2 sides: line segment? (twice drawn)
Which is, BTW, essentially like a degenerate (b=0) ellipse.
I wouldn't call it a line segment. Let's let bigons be bigons!
> With 1 side (but closed, as polygons of 3 or more sides): ???????
> What would it be called? A monogon? A monoangle?
Or a unigon.
> It wouldn't be a line segment (as the bigon/biangle), because a line
> segment has 2 vertexes, its endpoints.
>
> Calling a line segment a bigon/biangle is a stretch in itself, though I
> might have seen this before.
>
> And, last question, if a monogon/monoangle is simply a point,
Oh, a unigon is not simply a point, anymore than a bigon is simply a line
segment! A unigon has a side (albeit of length 0), a simple point doesn't.
> how is this to be distinguished from a 0-sided polygon?
That's easy. It has no vertex either! You can't see it.
Cheers,
David
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>From: David W. Cantrell DWCan...@sigmaxi.org
>Date: 6/27/2002 7:29 PM Central Standard Time
>Message-id: <20020627202937.905$u...@newsreader.com>
>
>qqq...@mindspring.com (Leroy Quet) wrote:
>> This question has been inspired more by the poetic half of my brain,
>> rather than the mathematical side.
>>
>> A polygon with 4 sides: quadrilateral
>>
>> A polygon with 3 sides: triangle
>>
>> With 2 sides: line segment? (twice drawn)
>
>Which is, BTW, essentially like a degenerate (b=0) ellipse.
>
>I wouldn't call it a line segment. Let's let bigons be bigons!
>
>> With 1 side (but closed, as polygons of 3 or more sides): ???????
>
>> What would it be called? A monogon? A monoangle?
>
>Or a unigon.
Not an -igon?
William Elliot
> A polygon with 4 sides: quadrilateral
> A polygon with 3 sides: triangle
> With 2 sides: line segment? (twice drawn)
_ I wouldn't call it a line segment. Let's let bigons be bigons!
ROFL.
> With 1 side (but closed, as polygons of 3 or more sides): ???????
> What would it be called? A monogon? A monoangle?
_ Or a unigon.
_ Oh, a unigon is not simply a point, anymore than a bigon is simply a
_ line segment! A unigon has a side (albeit of length 0), a simple
_ point doesn't.
-)
> how is this to be distinguished from a 0-sided polygon?
_ That's easy. It has no vertex either! You can't see it.
Ha, of course, it's a nogon. -)
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Doug Magnoli
"David W. Cantrell" wrote:
> qqq...@mindspring.com (Leroy Quet) wrote:
> > This question has been inspired more by the poetic half of my brain,
> > rather than the mathematical side.
> >
> > A polygon with 4 sides: quadrilateral
> >
> > A polygon with 3 sides: triangle
> >
> > With 2 sides: line segment? (twice drawn)
>
> Which is, BTW, essentially like a degenerate (b=0) ellipse.
>
> I wouldn't call it a line segment. Let's let bigons be bigons!
I hate puns, but this one is good.
>
>
> > With 1 side (but closed, as polygons of 3 or more sides): ???????
>
> > What would it be called? A monogon? A monoangle?
>
> Or a unigon.
Now David, I expect more from you. You've seriously disillusioned me. All
those -agons (not -igons, btw) (except that we don't talk about polyagons,
but I expect that has to do with the vowel that comes built-in when you get
poly-.) are Greek. We don't speak of quadragons or sexagons. (Probably
because it would be so hard to deal with in high school classrooms.) Just
the -ilaterals are Latin, although it seems that there are only one of them.
(Never heard of a octilateral. Sounds like something you should have removed
before it becomes serious.) So your pun has just changed to letting digons
be digons, which loses something somehow.
>
>
> > It wouldn't be a line segment (as the bigon/biangle), because a line
> > segment has 2 vertexes, its endpoints.
> >
> > Calling a line segment a bigon/biangle is a stretch in itself, though I
> > might have seen this before.
Yes, this is a problem--but I think it can be solved by David's method with
the monagon. A line segment doesn't have any vertices, whereas somehow a
monagon has one. (I'm not sure where it is--maybe you have to connect the
monogon to itself, ending up with a circle-like thing, but be sure to put a
kink in it where it connects to itself. But a circle-like thing has too much
interior, it's too big, so you can shrink down one of its semi-axes to zero,
and you're back to your monogon. Only this time it clearly has one vertex.)
>
> >
> > And, last question, if a monogon/monoangle is simply a point,
>
> Oh, a unigon is not simply a point, anymore than a bigon is simply a line
> segment! A unigon has a side (albeit of length 0), a simple point doesn't.
Your distinction is a good one. Of course, the difficulty comes when you're
walking down the street on a Tuesday afternoon and run into one of these.
Without the box it came in, you have no way of being able to tell whether it
has a side of length zero or no side at all. Moral: think twice before
throwing away the box.
-Doug Magnoli
[Delete the two and the three for email.]
Paul Hughett
: This question has been inspired more by the poetic half of my brain,
: rather than the mathematical side.
: A polygon with 4 sides: quadrilateral
: A polygon with 3 sides: triangle
: With 2 sides: line segment? (twice drawn)
: With 1 side (but closed, as polygons of 3 or more sides): ???????
: Of course, such a polygon does not exist in the REAL world.
: But what about in an abstract sense?
: Of course, of course....
: What would it be called? A monogon? A monoangle?
A n-sided polygon can also be called a n-gon. (Well, actually "-gon"
translates as angle, so "n-angled polygon" might be more appropriate.)
If you want a non-symbolic name, you should use the Greek prefixes to
match the pattern of pentagon, hexagon, heptagon, etc. Hence,
counting down we have pentagon, tetragon, trigon, bigon, monogon. I
don't know enough Greek to render 0-gon, but nogon sounds nice even if
it isn't regular.
Conversely, you could count sides instead, in which case quadrilateral
suggests using Latin prefixes. Hence unilateral, bilateral,
trilateral, quadrilateral, quinquelateral, sexalaterial, septalateral,
octalateral, etc.
: It wouldn't be a line segment (as the bigon/biangle), because a line
: segment has 2 vertexes, its endpoints.
A bigon contains two line segments AB and CD placed such that that the
vertices B and C are coincident and D and A are coincident. This
requires that the segments themselves are coincident so that a bigon
is distinguished from a line segment only in its logical structure but
not by the points it contains.
: Calling a line segment a bigon/biangle is a stretch itself, though I
: might have seen this before.
The logical structures are distinct, although the pointsets are the same.
: And, last question, if a monogon/monoangle is simply a point, how is
: this to be distinguished from a 0-sided polygon?
A monogon is a single line segment AB such that A and B are
coincident. A nogon is a set of no line segments and is thus easily
distinguished from a monogon.
Paul Hughett
A N Neil
> With 2 sides: line segment? (twice drawn)
Anthony Buckland
>DWCan...@sigmaxi.org
>
>> ...
>>What would it be called? A monogon? A monoangle?
>>
> _ Or a unigon.
> ...
>
>You can't see it.
> ...
>
Nobody (except maybe Ally McBeal) sees unigons any more.
They were hunted to extinction for the questionable medications
that could be made from their single vertices.
Chergarj
all = none or zero
allgon
G C
Renny
"goes-on-an'-on-agon"...
...or perhaps because all one-sided and two-sided polygons have no
area then they're not visible and so are just "gon"... (groan!)
Andy Spragg
of the queue on 28 Jun 2002 00:29:37 GMT, and nailed this to the shed
door:
^ qqq...@mindspring.com (Leroy Quet) wrote:
^ > This question has been inspired more by the poetic half of my brain,
^ > rather than the mathematical side.
^ > A polygon with 4 sides: quadrilateral
^ >
^ > A polygon with 3 sides: triangle
^ >
^ > With 2 sides: line segment? (twice drawn)
^
^ Which is, BTW, essentially like a degenerate (b=0) ellipse.
^
^ I wouldn't call it a line segment. Let's let bigons be bigons!
Aaaarrggh!
Andy
--
sparge at globalnet point co point uk
"Ignorance is linked to laziness, both are deplorable,
the latter not to be confused with tuit-shortage,
which looks a lot like laziness to the ignorant"
Austin Shackles, uk.rec.sheds
Bill Taylor
|> Nobody sees unigons any more.
|> They were hunted to extinction for the questionable medications
|> that could be made from their single vertices.
Oh. You haven't been to central Tibet recently then?
/
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David W. Cantrell
> "David W. Cantrell" wrote:
> > qqq...@mindspring.com (Leroy Quet) wrote:
> > > With 1 side (but closed, as polygons of 3 or more sides): ???????
> >
> > > What would it be called? A monogon? A monoangle?
> >
> > Or a unigon.
>
> Now David, I expect more from you.
I also expect more from myself! What was I thinking?
Perhaps I should plead temporary insanity.
> You've seriously disillusioned me.
Hmm. If you thought that I never make mistakes, then you had disillusioned
yourself! Humans err.
I agree that it's normally nicest to form words using roots from a single
language. For example, I recently noted in the thread "QUINTICS" that
"superradical" should be preferred to "hyperradical".
Of course, I suppose it could be argued that avoiding words "of mixed
parentage" is just being old-fashioned. There is some precedence
for such words among mathematical terms. "Hexadecimal" comes to
mind, for example. (Purists should insist on "sexadecimal"! Are you
listening, Thinkit?)
> All those -agons (not -igons, btw) (except that we don't talk about
> polyagons, but I expect that has to do with the vowel that comes built-in
> when you get poly-.) are Greek. We don't speak of quadragons or
> sexagons. (Probably because it would be so hard to deal with in high
> school classrooms.) Just the -ilaterals are Latin, although it seems
> that there are only one of them. (Never heard of a octilateral. Sounds
> like something you should have removed before it becomes serious.) So
> your pun has just changed to letting digons be digons, which loses
> something somehow.
Agreed. "Digon" is correct. (I believe that someone earlier in the thread
even gave a reference for "digon" at MathWorld.) And similarly it seems
that we should, as you said, use "monagon". But more about that later.
BTW, there are other options. We could, for example, use "bilateral"
and "unilateral" as nouns, like "quadrilateral". But note that, if we
chose these terms, there would be a shift in the sense of the words.
Instead of indicating the number of angles, they would indicate the
number of sides.
> > > It wouldn't be a line segment (as the bigon/biangle), because a line
> > > segment has 2 vertexes, its endpoints.
> > >
> > > Calling a line segment a bigon/biangle is a stretch in itself, though
> > > I might have seen this before.
>
> Yes, this is a problem--but I think it can be solved by David's method
> with the monagon. A line segment doesn't have any vertices, whereas
> somehow a monagon has one. (I'm not sure where it is--maybe you have to
> connect the monogon to itself, ending up with a circle-like thing, but be
> sure to put a kink in it where it connects to itself. But a circle-like
> thing has too much interior, it's too big, so you can shrink down one of
> its semi-axes to zero, and you're back to your monogon. Only this time
> it clearly has one vertex.)
>
> > > And, last question, if a monogon/monoangle is simply a point,
> >
> > Oh, a unigon is not simply a point, anymore than a bigon is simply a
> > line segment! A unigon has a side (albeit of length 0), a simple point
> > doesn't.
>
> Your distinction is a good one. Of course, the difficulty comes when
> you're walking down the street on a Tuesday afternoon and run into one of
> these. Without the box it came in, you have no way of being able to tell
> whether it has a side of length zero or no side at all. Moral: think
> twice before throwing away the box.
Let's consider various thing about these degenerate cases.
Name: Digon
Vertices: Two
Sides: Two, which coincide
Perimeter = 2*d where d is the distance between the vertices
Angles: Two, both 0
N.B. The later observation is important for the name "digon" to be
correct. Also, it works well with the fact that the sum of the angles
in an N-gon is pi*(N-2).
Proposed name: Monagon
Vertices: One vertex
Sides: One side (of length 0)
Perimeter = 0
Angles: ???
Perhaps there is no problem with saying that a degenerate case has
one vertex and one side of length 0. But I do have a problem with the
idea that there would be any angle involved, regardless of its measure.
For an angle to be formed, do we not need two sides? With the digon,
we have two sides, each used to form two angles of measure zero with
the two different vertices. But with the proposed "monagon", it seems
to me that there can be no angle whatsoever. Thus, if this degenerate
case is to be considered at all, perhaps "unilateral" would be a good
name. As a further argument against associating any angle with this
case, note that, with N=1 in the formula pi*(N-2), we get a _negative_
result.
Methinks it best to consider N-gons only for natural N >= 2.
Joseph Hertzlinger
On 05 Jul 2002 20:33:03 GMT, David W. Cantrell
<DWCan...@sigmaxi.org> wrote:
>I agree that it's normally nicest to form words using roots from a
>single language. For example, I recently noted in the thread
>"QUINTICS" that "superradical" should be preferred to "hyperradical".
Do you drive a suimobile?
David W. Cantrell
No. I drive a car.
Cheers,
Matthew Montchalin
What, for hauling swine?
Or did you mean 'ipsimobile?'