NationStates Jolt Archive

I've always wondered about this. Is it a one sided figure? I've also heard that it's a figure of infinite sides.

∞

A circle has two sides.

In side
Out side

A circle has two sides.

In side
Out side

it can have an up side and a down side and an inside and outside

Infinite

2 - good and bad.

∞
Does this mean that a circle is a polygon?

apart from the hilarious starter

"How many sides does a circle have?
My son answered "infinate" on a test and was corrected. [of course. there is no such thing as infinate sides]

here (http://mathcentral.uregina.ca/QQ/database/QQ.09.00/georganne1.html)is a nice link where everyone in this thread so far can be right.

A circle by definition is not a polygon, and thus has no sides at all. While circle-like polygons can be created with millions or billions of sides, under a microscope it still won't be a circle. (For that reason, circles are impossible to draw accurately, and we can only approximate by drawing 60000-sided polygons or so.)

Does that help?

∞

A circle has two sides.

In side
Out side

By that definition, a triangle would have six sides.

A circle has one side.

By that definition, a triangle would have six sides.
Huh?

I've always wondered about this. Is it a one sided figure? I've also heard that it's a figure of infinite sides.

2. Inside and outside.

I've always wondered about this. Is it a one sided figure? I've also heard that it's a figure of infinite sides.

A circle can be considered to be a polygon of infinite sides, since each 'point' of the circle circumference might be assumed to be one 'side'.

On the other hand, if a circle is considered to have 'curved' sides, then it only really contains one 'side'. (Or, I guess, and infinite number of small curves).

There is a certain logic to assuming that a circle is actually an 'infinite' polygon... one can compare the perimeters of polygons to their area, and find that: if we keep the perimeter constant, the area increases incrementally with the addition of 'sides'.

The area increases as the figure approximates 'circular'... thus, it could be argued that the 'peak' perimeter-to-area polygon, is one which is (effectively) a circle.

A circle by definition is not a polygon, and thus has no sides at all. While circle-like polygons can be created with millions or billions of sides, under a microscope it still won't be a circle. (For that reason, circles are impossible to draw accurately, and we can only approximate by drawing 60000-sided polygons or so.)

I think you've actually just proved that circles do not exist!

A circle can be considered to be a polygon of infinite sides, since each 'point' of the circle circumference might be assumed to be one 'side'.

Can you really say that, with a 'point' being defined as not having "area"/not occupying "space" (I'm sorry, my English fails me at correct mathematical expressions) ? Also, see the Czardanian post about circles not being polygons.

I think you've actually just proved that circles do not exist!

....Well, yeah....then again anything that isn't at least 4 dimensional doesn't exist either...

Can you really say that, with a 'point' being defined as not having "area"/not occupying "space" (I'm sorry, my English fails me at correct mathematical expressions) ? Also, see the Czardanian post about circles not being polygons.

Well, the sides of your average polygons are line segments which don't take up any space either....

Can you really say that, with a 'point' being defined as not having "area"/not occupying "space" (I'm sorry, my English fails me at correct mathematical expressions) ? Also, see the Czardanian post about circles not being polygons.

I hear what Czardas is saying... but, when two things are incapable of being differentiated, they are effectively the same.

Thus, a 'polygon of infinite number of sides' (the theoretical upper 'limit' of polygon nodality) would be, effectively, a circle.

I'm not really claiming that the 'points' would have an area... they just represent infinitely small vectors, corresponding to infinitely multiple sides.

Is a circle a polygon where number of sides (n) = infinity?

If it walks like a circle, and quacks like a circle...

I think you've actually just proved that circles do not exist!
It's been the best answer so far.

I think it's usually taught that a circle has one side, but now that I think about it, the infinite points on a circle would make an infinite amount of sides. Boggles the mind, doesn't it? They should get the world's mathematicians on this instead of pi.

*Gasp* What if pi leads to the answer of how many sides a circle has?

Depending on your definition of a side, a circle has either 0, 1 or infinite sides. Someone search for the proper definition by Euclid, that should give us an answer.

actually, if it's infinite, that would also imply that it also have an infinite number of angles, which would be 0.0 recuring smaller than a 180 degree angle, and thus 180 degree angles. If that's the case, then all shapes have infinite sides.

The amount of sides a circle has is defined by ones reality. It can have no sides or infinite. Perspective is the key factor.

actually, if it's infinite, that would also imply that it also have an infinite number of angles, which would be 0.0 recuring smaller than a 180 degree angle, and thus 180 degree angles. If that's the case, then all shapes have infinite sides.

Is this thread going to be going into calculus in the next couple of pages? Because I haven't learned that yet....

Well, the sides of your average polygons are line segments which don't take up any space either....
Point taken.

The goal of Maths is to give absolutes.

All I care about is the prevailing legal definition of a circle. I'll work from whatever that is. (hehehehehe)

..but, when two things are incapable of being differentiated, they are effectively the same.
Generalist!
Seriously, when does "incapability of differentiating" start? 'Cause if you want to be smart-ass enough, you can always go one step further..?

Thus, a 'polygon of infinite number of sides' (the theoretical upper 'limit' of polygon nodality) would be, effectively, a circle.
That's the thing, would it really, or could you just say "well, I'll just step my theoretical distinguishing abilities up a notch.."

I'm not really claiming that the 'points' would have an area... they just represent infinitely small vectors, corresponding to infinitely multiple sides.
I see the vector thing, but vector=side?

If it walks like a circle, and quacks like a circle...
Your circles walk and quack? You might want to stop looking at the screen and take a deep breath..

I think it depends on what you're using; if you were to make a circle out of points that had no space between them that were all equidistant from the center point, you would have no sides.

Or, if you were to construct a circle out of small shapes and use them to form the circle, taking the limit to infinity of the sum of the areas of the shapes would eventually produce a number equal to the area of the circle you desire.

However, the distance between the points would become infintesimally small but nonzero making the number of sides infinite...so it's possible to either have no sides or infinite sides and still produce the same shape.

Holy mathematical wanking, batman!

How many sides does a circle have?
Depends on the resolution of your monitor.

A circle is 2 dimensional, therefore it has 2 sides, front and back.

actually, if it's infinite, that would also imply that it also have an infinite number of angles, which would be 0.0 recuring smaller than a 180 degree angle, and thus 180 degree angles. If that's the case, then all shapes have infinite sides.

If you're constructing the area (and by extension the shape itself) out of the Riemann sum of the equation that models the shape, that is true because there are an infinite number of shapes of an infintesimally small but nonzero width that make up the larger one making the shape have an infinite number of sides.

This assumes a "side" is a line segment between to points, for example x and x+δx.

Damn, wish there was Latex script on Jolt...

A circle is 2 dimensional, therefore it has 2 sides, front and back.

How do you see the back of a shape without depth? :p

A circle is 2 dimensional, therefore it has 2 sides, front and back.

Well....A square is two dimensional, but we tend to agree it has four sides.

Damn, wish there was Latex script on Jolt...

mmmm.. kinky...

Generalist!
Seriously, when does "incapability of differentiating" start? 'Cause if you want to be smart-ass enough, you can always go one step further..?


No - we are looking at the pinnacle of polygons, effectively... the point where our progression in number-of-sides has reached it's peak (which is, of course, theoretical.... because you can only ever approximate infinity... but then again, we can only ever actually 'approximate' a circle, too).

When you reach that point with your polygon versus circle comparison, where the divergence is tending to zero, the difference between forms is tending towards infinitely small, and the degree of approximation is the same... you are, effectively, talking about the same figure.


That's the thing, would it really, or could you just say "well, I'll just step my theoretical distinguishing abilities up a notch.."


But, I'm not talking about a 'big number'... I am talking about infinite sides. It doesn't matter how far up you step your distinguishing abilities, we are talking about an effective infinite number.


I see the vector thing, but vector=side?


I'm claiming a 'side' wherever the 'vector' is altered... thus, at each 'corner' (for want of better terms), a new vector is formed, and a new 'side' is determined.


Your circles walk and quack? You might want to stop looking at the screen and take a deep breath..

Your circles don't walk and quack? Maybe that's the problem... :)

mmmm.. kinky...

I know...the antiderivative of the natural logarithmic functions...nipples could cut glass right now...:eek:

I know...the antiderivative of the natural logarithmic functions...nipples could cut glass right now...:eek:

Dangit! I knew we were going into calculus.....stupid education...I could be learning it already...

Am I mistaken, or do people usually consider a cylinder to have 3 sides...

No - we are looking at the pinnacle of polygons, effectively... the point where our progression in number-of-sides has reached it's peak (which is, of course, theoretical.... because you can only ever approximate infinity... but then again, we can only ever actually 'approximate' a circle, too).
That's all I wanted to hear. Thanks, Uncle Gravy.

Your circles don't walk and quack? Maybe that's the problem... :)
They do now.
/troubleshooting

Am I mistaken, or do people usually consider a cylinder to have 3 sides...
3 faces. 2 sides, maybe?

I'm claiming a 'side' wherever the 'vector' is altered... thus, at each 'corner' (for want of better terms), a new vector is formed, and a new 'side' is determined.

You're assuming that a side can necessarily be defined by a vector, but if a curve can be used to mean a side, you can't do that. Unless you're stating that you assume that, in which case you'd have 0 sides, as none of the sides of a circle can be described by a vector (other than (0,0)).

3 faces. 2 sides, maybe?

True, which would mean that a circle has 1 side...

It has no sides. One of the requisite features of a side is that it opposes another side.Circles have a continuous cylindrical plane. No sides.

It has no sides. One of the requisite features of a side is that it opposes another side.Circles have a continuous cylindrical plane. No sides.

Eh? What do you mean "opposes another side"?

Either I'm misunderstanding you, or triangles don't have sides either...

Circles don't have sides, they have complications.

Either I'm misunderstanding you, or triangles don't have sides either...

it's a misunderstanding. the sides of a triangle do oppose each other, but are not diametrically opposite. they are joined by an angle and not an arc.

You could say the same for sides of a circle if it has infinite sides.

Depends on your definition of side I'd say~

Like whether sides can curve or not, and other stuffs. And as far as I know, there is at this moment no perfect definition of side available that can be applied to circles (I'm not sure though). So I think it kinda depends on who you're talking to.

Proof for infinite sides, as limitsituation of a polygon, circle defined as the collection of points at the same distance to a central point:
In a 2D-ploygon (however you may call that ), the distance to the corners is always greater than the distance to the edges. The relation between those 2 can be computed as: (distance to corner)/(distance to edge)=1/cos(360°/2n)
When n becomes very large, 360/2n becomes very near to zero, so in the limit it will be zero. With cos(0)=1, we can conclude:
(distance to corner)/(distance to edge)=1 or (distance to corner) = (distance to edge). If that is true, that means that the distance to every point is the same, a thingie like that is called a circle ^_^.

you can draw in infinite number of lines tangent to a circle. Ie. a circle has in infinite number of infinitessimally small sides. The argument that a circle is not a polygon and so has no sides is flawed, as that would make it a 1 dimensinal figure. A 1 dimensional figure cannot have a width. A circle has both length and width (though they are always the same value), and so is a 2 dimensional figure, ergo a polygon posessed of an infinite number of sides. And just to prevent at least one argument to this: a square also has identical length and width. And before anyone says that there are no points on a circle: a circle has an infinite number of points.

it's a misunderstanding. the sides of a triangle do oppose each other, but are not diametrically opposite. they are joined by an angle and not an arc.

Well....if a circle has infinite sides, they oppose another, so they are sides. If it has no sides it doesn't oppose....and there aren't sides.....If it has sides, it has sides, and if it doesn't have sides it doesn't have sides. Got it.

I would say no sides. (thinks back to geometry) I think a side is by definition linear. A curve is not a side, but a continuous string of points.

This is from rote memory from eight years ago, so I could be wrong.

Remains to be decided if a circle is a polygon and, if so, if it has corners...

you can draw in infinite number of lines tangent to a circle. Ie. a circle has in infinite number of infinitessimally small sides. The argument that a circle is not a polygon and so has no sides is flawed, as that would make it a 1 dimensinal figure. A 1 dimensional figure cannot have a width. A circle has both length and width (though they are always the same value), and so is a 2 dimensional figure, ergo a polygon posessed of an infinite number of sides. And just to prevent at least one argument to this: a square also has identical length and width. And before anyone says that there are no points on a circle: a circle has an infinite number of points.

Well....a circle is and infinite number of points....Same thing though.

You're assuming that a side can necessarily be defined by a vector, but if a curve can be used to mean a side, you can't do that. Unless you're stating that you assume that, in which case you'd have 0 sides, as none of the sides of a circle can be described by a vector (other than (0,0)).

Well... the vector argument here is designed to correspond to the assumption of infinite points joined by infinite 'sides'... where each side represents a vector between nodes.

Remains to be decided if a circle is a polygon and, if so, if it has corners...

Doesn't polygon mean "many-sides/sided" or something like that? So if it has sides it's a polygon, if it doesn't, it isnt....<_>

Can't you draw an infinite amount of tangents to an angle?

Can't you draw an infinite amount of tangents to an angle?

To an angle? As in...like...two rays coming from the same point or something like that? I suppose with an arc you could....

But, as you can only find one tangent to each point, none of them can be angles... so, infinite sides but no angles... but that doesn't make sense because none of the sides would actualy connect anywhere. Where's my flaw plz :confused:

That's all I wanted to hear. Thanks, Uncle Gravy.


They do now.
/troubleshooting

Uncle Gravy? :D

Most welcome. It's true though... perhaps moreso for the circle than for any other figure... I guess you could have a 'theoretically' perfect circle, by virtue of an (infinitely) precise equation.... but your 'physical' circle corresponding to your math would be inherently flawed by it's attempt to express a perfect curvature...

There is such a thing as a perfect circle. It is, in fact, the equation, as you can't seem to describe it properly geometrically.

But, as you can only find one tangent to each point, none of them can be angles... so, infinite sides but no angles... but that doesn't make sense because none of the sides would actualy connect anywhere. Where's my flaw plz :confused:

Umm.....I have no idea what you are saying....so I'll just muse a bit on random things...for a infinite sided thingy...the interior angles would all be 180 degrees, and the exterior would be 0..or infintesimal or something, I dunno... What are you saying?

umm... the conclusion i'm currently getting to is: infinite sides, infinite number of 180 degree angles, nothing else. Same as a straight line in fact...

There is such a thing as a perfect circle. It is, in fact, the equation, as you can't seem to describe it properly geometrically.

it exists...as like, a concept, and can be represented numerically and stuff....but can't be depicted, much less created....like a hypercube....Then there's things you can depict but still can't create, like those impossible figure things you see in optical illusion books....

..It's true though... perhaps moreso for the circle than for any other figure... I guess you could have a 'theoretically' perfect circle, by virtue of an (infinitely) precise equation.... but your 'physical' circle corresponding to your math would be inherently flawed by it's attempt to express a perfect curvature...
See, that's what I thought. I dwelled in the higher spheres of the perfect, theoretical circle and never bothered with earthly scum such as physicalization.

My math teachers made me learn damn quickly that anything physical in maths were flawed and that I needed to let go of any rationale based on that physical things when wanting to think mathematically, so..

See, that's what I thought. I dwelled in the higher spheres of the perfect, theoretical circle and never bothered with earthly scum such as physicalization.

My math teachers made me learn damn quickly that anything physical in maths were flawed and that I needed to let go of any rationale based on that physical things when wanting to think mathematically, so..

Even when you have 2 apples and someone gives you 3 more apples, then you have 5 apples? That's flawed too? :eek:

Even when you have 2 apples and someone gives you 3 more apples, then you have 5 apples? That's flawed too? :eek:

Actually, empirically.... yes. Our 'apple' in the above example is an approximation... there is no one 'precise' value implied, and we are introducing our own assumed rounding-errors. (Example, if one of the apples is lightly damaged, is it not, really 'less' of an apple?)

Actually, empirically.... yes. Our 'apple' in the above example is an approximation... there is no one 'precise' value implied, and we are introducing our own assumed rounding-errors. (Example, if one of the apples is lightly damaged, is it not, really 'less' of an apple?)

*GASP!* The foundations of my mathmatical thought! NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!

*cough* Yeah...not really....But still, that's....intresting...Meh, It still taught me long division, I'm okay with it.

Even when you have 2 apples and someone gives you 3 more apples, then you have 5 apples? That's flawed too? :eek:
Yes, because no two apples are the same, yet you/we assume equal units to be added/dealt with.

edit// been beating to it, eh?

...Meh, It still taught me long division, I'm okay with it.Apples did? May I ask whether Uncle Gravy and you are from the same country, where long division is done through amassing of apples and circles walk an quack..?

Apples did? May I ask whether Uncle Gravy and you are from the same country, where long division is done through amassing of apples and circles walk an quack..?

Well, It wasn't really apples as much as it was red, green and blue dots on a peice of graphing paper....but same idea...

Yes, because no two apples are the same, yet you/we assume equal units to be added/dealt with.

edit// been beating to it, eh?

Great minds think alike, no?

As soon as it has a number of sides, it would be better referred to as an (insert number here)gon. Would infinite sides become an infinigon? I hope so, I like that word.

Apples did? May I ask whether Uncle Gravy and you are from the same country, where long division is done through amassing of apples and circles walk an quack..?

They don't do it that way, elsewhere?

As soon as it has a number of sides, it would be better referred to as an (insert number here)gon. Would infinite sides become an infinigon? I hope so, I like that word.

...That would be cool. I'd never use the word circle again....In fact, from now on I'm using the word "infinigon" in place of circle.

...That would be cool. I'd never use the word circle again....In fact, from now on I'm using the word "infinigon" in place of circle.

Sweet. Spread the word and tell 'em Mega sent'ya.

I say it depends on how steady your hand is when you draw the circle.

THINK LESS, LIVE MORE!

I say it depends on how steady your hand is when you draw the circle.

THINK LESS, LIVE MORE!

Ummm....I don't think you'd want tell people to think less, we do little enough of it as is.

A circle can be considered to be a polygon of infinite sides, since each 'point' of the circle circumference might be assumed to be one 'side'.
Are you sure that you can consider each single point a side? It would seem to me that it would make more sense to assume each two points formed a side, which would still give you a polygon of infinite sides, but that's just a guess.

Are you sure that you can consider each single point a side? It would seem to me that it would make more sense to assume each two points formed a side, which would still give you a polygon of infinite sides, but that's just a guess.

Well, they would define a side, so I suppose that works too...

circles have no sides, sides have to be line segments.

Are you sure that you can consider each single point a side? It would seem to me that it would make more sense to assume each two points formed a side, which would still give you a polygon of infinite sides, but that's just a guess.

Ah... each 'point' is the side between two lesser 'points'....

Well, It wasn't really apples as much as it was red, green and blue dots on a peice of graphing paper....but same idea...
Oh, we were never allowed to do dots, we had to do x.

Great minds think alike, no?
Far be it from me to accept such ridiculous praise as to liken the image of my mind to yours. You must have lost that remaining ounce of a grasp of reality now.


They don't do it that way, elsewhere?
No, Hitler abolished that and somehow we neglected to introduce it again after the liberation. Lost in transition, or something.

THINK LESS, LIVE MORE!
Umm..see, you're on General. Thinking is rare, and lives we don't have.

circles have no sides, sides have to be line segments.
And a point isn't an ultimatively small line segment?

Also: source?

(I checked the Elements, none of the 23 definitions deal with "side" )

Well, It wasn't really apples as much as it was red, green and blue dots on a peice of graphing paper....but same idea...

Oh, we were never allowed to do dots, we had to do x.




Dina? I'm a girl now?

circles have no sides, sides have to be line segments.

Eh, a point is a line segment with a length of 0, how's that?

Dina? I'm a girl now?
a) I never assume. Why shouldn't you?
b) Why should Dina make you a girl?
c) You put the line segment/point thing better than I did :)

Far be it from me to accept such ridiculous praise as to liken the image of my mind to yours. You must have lost that remaining ounce of a grasp of reality now.


See... now it is I that is being the recipient of undeserved praise. :)

Less of your modesty, friend... The forum would be a darker place, without you. :)


No, Hitler abolished that and somehow we neglected to introduce it again after the liberation. Lost in transition, or something.


Hitler abolished apple-division and quacking circles? I mean... I knew he was a fiend and all.... but...


Umm..see, you're on General. Thinking is rare, and lives we don't have.

Hey! I have a life!

Wait... I just Googled it... what I've got is a 'knife'. Carry on.

Eh, a point is a line segment with a length of 0, how's that?

A point is not a line. A line (segment) is composed of an infinite number of points. A circle has an infinite number of points and an infinite number of line segments, each with a length that is infintesimally small.

Eh, a point is a line segment with a length of 0, how's that?

This, I like. :)

Edit: SoWiBi beat me to it, this time.

A point is not a line. A line (segment) is composed of an infinite number of points. A circle has an infinite number of points and an infinite number of line segments, each with a length that is infintesimally small.

How has nobody said this yet, every shape has an infinite number of points. If every point constitutes a side, as someone said, I think, it's late and all this math is melting my brain, then a square has an infinite number of sides, as does a triangle, as does a line, as does anything which contains points.

Less of your modesty, friend... The forum would be a darker place, without you.
Light is overrated and just makes your eyes itch after a while.
And shut it already, or I'll call the mods for blush-bait.

Hitler abolished apple-division and quacking circles? I mean... I knew he was a fiend and all.... but...
Yeah, them apples looked too Jewish and quacking circles had that faggy air.

Hey! I have a life!
Wait... I just Googled it... what I've got is a 'knife'. Carry on.
Hands down, you win.
Edit: SoWiBi beat me to it, this time.
Jolt are equal opportunity post hosters. *nods*

A point is not a line. A line (segment) is composed of an infinite number of points. A circle has an infinite number of points and an infinite number of line segments, each with a length that is infintesimally small.

Wait...the length of the line segments of a circle are infinetesimal, but not 0? because if the length of a line segment were zero, it'd be a 0 dimensional, a point.I figure a point is a line of 0 length, like a line is a square of 0 width, or a square a cube of 0 depth.....(or a cube a...hypercube, if you will, of 0.....time. That's the fourth dimension, yes?)

How has nobody said this yet, every shape has an infinite number of points. If every point constitutes a side, as someone said, I think, it's late and all this math is melting my brain, then a square has an infinite number of sides, as does a triangle, as does a line, as does anything which contains points.

assuming a line segment is indeed comprised of infinite points, and that each point constitutes a side in the case of a square....

Perhaps it makes more sense when we consider a side between each pair of adjacent points rather than the actual points themselves...

∞
A circle has two sides.

In side
Out side
Both are correct, but ∞ would be preferred by me.

Light is overrated and just makes your eyes itch after a while.
And shut it already, or I'll call the mods for blush-bait.


Actually, I think I could make a fairly good argument that it was you, not I, that began the blush-baiting... :D

I am an innocent victim...


Hands down, you win.


Hey... we have to get our giggles somehow... :)

Actually, I think I could make a fairly good argument that it was you, not I, that began the blush-baiting... :D
Ah no, a lady never would.

I am an innocent victim...
Anybody else heard 'innocent' ?

Both are correct, but ∞ would be preferred by me.
Now, there's my ex math teacher breathing down my neck again, telling me once and for all that in math, every true statement is true to the exclusion of all others who say different..[/ rotten English], meaning that "2" and "infinite number" couldn#t be "both correct" ?

Wait...the length of the line segments of a circle are infinetesimal, but not 0? because if the length of a line segment were zero, it'd be a 0 dimensional, a point.I figure a point is a line of 0 length, like a line is a square of 0 width, or a square a cube of 0 depth.....(or a cube a...hypercube, if you will, of 0.....time. That's the fourth dimension, yes?)

I think you got the first part right. But is time really the 4th dimension, or is that something that a lot of people said and it caught on, regardless if it's true or not? How do you define a dimension, anyway?

Ah no, a lady never would.


Then, as the gentleman, I must admit that it was I that was at fault... despite the fact that I have a conviction that, just perhaps... it was I who was driven to blushes first....


Anybody else heard 'innocent' ?


Hey! There are LOTS of things I am innocent of! Dozens, maybe! :o

Then, as the gentleman, I must admit that it was I that was at fault... despite the fact that I have a conviction that, just perhaps... it was I who was driven to blushes first....
I shall not be held accountable for what drives you to blushes.

Hey! There are LOTS of things I am innocent of! Dozens, maybe! :o
Maybe. And in another dimension.

I shall not be held accountable for what drives you to blushes.


On the contrary, I am scandalised to hear you say as much... after all, every lady knows that a mere male will be driven to distraction by flattering descriptions of the size of his.... intellect. :o


Maybe. And in another dimension.

This would be that fourth dimension, yes? (See, I am on topic...)

I think you got the first part right. But is time really the 4th dimension, or is that something that a lot of people said and it caught on, regardless if it's true or not? How do you define a dimension, anyway?

Well...It makes sense to me...It can be measured, we can move through it....It could (and does) essentially act like any of our dimensions of space...We use units of time the same way we use units of length(/width/depth)

Well...It makes sense to me...It can be measured, we can move through it....It could (and does) essentially act like any of our dimensions of space...We use units of time the same way we use units of length(/width/depth)

I think the problem is the assertion of 'the' 4th dimension.... it seems logical that whichever 'dimension' is the 'first' to be tangential to the established three, must be a '4th dimension'. In some contexts that might refer to time, i suppose... in other contexts... maybe not so much?

Well… The circumference of a unit circle is equal to 2*pi

The perimeter of a unit polygon as a function of n sides is: p = n* sqrt(sin(2*pi/n)^2 + (1-cos(2*pi/n)^2)

In the limit as n approaches infinity, p approaches 2*pi

Therefore a polygon of n = infinity sides becomes indistinguishable from a circle.

I think the problem is the assertion of 'the' 4th dimension.... it seems logical that whichever 'dimension' is the 'first' to be tangential to the established three, must be a '4th dimension'. In some contexts that might refer to time, i suppose... in other contexts... maybe not so much?

Huh? :confused: Can we go over the tangential part again?

On the contrary, I am scandalised to hear you say as much... after all, every lady knows that a mere male will be driven to distraction by flattering descriptions of the size of his.... intellect. :o
It's not in my nature to dabble too much with male mating instincts, so I apologize for my ignorance. I shall refrain from stroking your..ego, then.

This would be that fourth dimension, yes? (See, I am on topic...)

I think the problem is the assertion of 'the' 4th dimension.. it seems logical that whichever 'dimension' is the 'first' to be tangential to the established three, must be a '4th dimension'. In some contexts that might refer to time, i suppose... in other contexts... maybe not so much?

Huh? :confused: Can we go over the tangential part again?

Well, you have your X dimension.... and your Y dimension intersects it, yes? Perpendicular to? And then, your Z dimension is at right angles to both X and Y, yes?

So... your next dimension would be the one that is tangential on that axis point.... the one that is at right angles to X, Y and Z, yes?

It's not in my nature to dabble too much with male mating instincts, so I apologize for my ignorance. I shall refrain from stroking your..ego, then.


My ego, then, shall remain 'unstroked'... and that, one assumes, is how you intend to spare my blushes? Thankfully, then, I shall be spared the embarrassment of a sudden, obvious, redistribution of blood.


I think the problem is the assertion of 'the' 4th dimension.. it seems logical that whichever 'dimension' is the 'first' to be tangential to the established three, must be a '4th dimension'. In some contexts that might refer to time, i suppose... in other contexts... maybe not so much?

Ooohh... that's me told...

Have you guys not figured this out yet?

*waits for answer to be revealed*

Well, you have your X dimension.... and your Y dimension intersects it, yes? Perpendicular to? And then, your Z dimension is at right angles to both X and Y, yes?
Yes.

So... your next dimension would be the one that is tangential on that axis point.... the one that is at right angles to X, Y and Z, yes?
*lets go of her constrcution with various CD cases to post*
Huh? I mean, I know I can't reconstruct a 4th dimension even with my coolest CD cases..but..I fail to imagine an axis point that it could/should be tangential to?

My ego, then, shall remain 'unstroked'... and that, one assumes, is how you intend to spare my blushes? Thankfully, then, I shall be spared the embarrassment of a sudden, obvious, redistribution of blood
Actually, coming to t hink of it, my plan fails. A redirection of the blood from the cheeks might be a damn good idea. Though I might be bound to do the sizeal praise again, then. Oh, between a rock and a hard place, I say.

Well, you have your X dimension.... and your Y dimension intersects it, yes? Perpendicular to? And then, your Z dimension is at right angles to both X and Y, yes?

So... your next dimension would be the one that is tangential on that axis point.... the one that is at right angles to X, Y and Z, yes?

Ah I see, Well, I thought about that, but I figure more that X, Y and Z (length witdh and depth I assume) make up Space in general, but then, take an object that exists in space, with some number greater than 0 for X, Y and Z. Then, after, How long, how wide, and How deep...I ask...When? The first three dimensions tell us where, and they can help you locate it's exact position....almost. It could be right there in 1987, but not there in 2004. the fourth dimension, like the other dimensions, should help us locate our object. The first three where it is, and because they are all part of answering the question "Where?" they happen to be perpendicular. Time would tell us when, and only time does that, unless there's another part to when something is, so it's linear, only one demensional, while Where comes about with three difeerent measurement, so it's....three dimensional.

As to how the fourth would relate with the other three...I see Time as a long tube of sorts (I know I said one-dimensional, but bear with me) and Space (Length Width Depth) move along the inside of tube, forwards or back, only one dimension.....


Well.....that's the first time I've ever written that out, hope it makes sense.

Have you guys not figured this out yet?

*waits for answer to be revealed*

Yes. Unfortunately, the answer was "orange".

So... now we are left trying to work out the question....

Well.....that's the first time I've ever written that out, hope it makes sense.

It makes sense to me. But I heard that there are (were, maybe) 11-13 dimensions or something. Anybody care to explain that one?

Yes. Unfortunately, the answer was "orange".

So... now we are left trying to work out the question....

"What is the most commonly known word that does not ryhme with anything?"

Have you guys not figured this out yet?

*waits for answer to be revealed*


Revelations are not the responsibility of this thread. (http://forums.jolt.co.uk/showpost.php?p=10473740&postcount=44)

It makes sense to me. But I heard that there are (were, maybe) 11-13 dimensions or something. Anybody care to explain that one?

Eh, I dunno, Most I've heard is that there's ten and the other six are curled up into them selves or something...

"What is the most commonly known word that does not ryhme with anything?"

Nah, I tend to think of purple before I think of orange.

Nah, I tend to think of purple before I think of orange.

What? Haven't watched enough TV to hear "Purple Nurple"?

*lets go of her constrcution with various CD cases to post*
Huh? I mean, I know I can't reconstruct a 4th dimension even with my coolest CD cases..but..I fail to imagine an axis point that it could/should be tangential to?


The axis point is easy... it intersects at the same point the other three do... the only problem is, trying to represent an angle that is perpendicular to X, Y, and Z, when you only have three avaliable dimensions...

It's like trying to climb into a three-dimensional box, that you just drew on a sheet of paper...


Actually, coming to t hink of it, my plan fails. A redirection of the blood from the cheeks might be a damn good idea. Though I might be bound to do the sizeal praise again, then. Oh, between a rock and a hard place, I say.

Sounds like a sizable risk... someone could get into trouble, that way...

Ah I see, Well, I thought about that, but I figure more that X, Y and Z (length witdh and depth I assume) make up Space in general, but then, take an object that exists in space, with some number greater than 0 for X, Y and Z. Then, after, How long, how wide, and How deep...I ask...When? The first three dimensions tell us where, and they can help you locate it's exact position....almost. It could be right there in 1987, but not there in 2004. the fourth dimension, like the other dimensions, should help us locate our object. The first three where it is, and because they are all part of answering the question "Where?" they happen to be perpendicular. Time would tell us when, and only time does that, unless there's another part to when something is, so it's linear, only one demensional, while Where comes about with three difeerent measurement, so it's....three dimensional.

As to how the fourth would relate with the other three...I see Time as a long tube of sorts (I know I said one-dimensional, but bear with me) and Space (Length Width Depth) move along the inside of tube, forwards or back, only one dimension.....


Well.....that's the first time I've ever written that out, hope it makes sense.

I understand, yes... but... it does rather rely on the assumption the three dimensions is 'all there is'... no?

What? Haven't watched enough TV to hear "Purple Nurple"?

Bah, not a real word. Give me one reputable dictionary that has nurple in it.

I understand, yes... but... it does rather rely on the assumption the three dimensions is 'all there is'... no?

How so? Perhaps all there is to space, to the question of "Where?", but there could be other things...all there is to what?

Bah, not a real word. Give me one reputable dictionary that has nurple in it.

Well, I don't have to:

http://www.googlefight.com/index.php?lang=en_GB&word1=orange&word2=purple

Orange is clearly more common than purple, thus it fits the answer of the question "What is the most commonly known word that does not ryhme with anything?" You're just weird. ^_^

Well, I don't have to:

Clearly, those results are skewed. Orange extremists were violently suppressing purple loyalists and voting multiple times. The orange-purple conflict is likely to start WWIII, so watch out.

Clearly, those results are skewed. Orange extremists were violently suppressing purple loyalists and voting multiple times. The orange-purple conflict is likely to start WWIII, so watch out.

Hmm, but what of the other secondary color, Green?

I've always wondered about this. Is it a one sided figure? I've also heard that it's a figure of infinite sides.

a side is a straight line therefore a circle has no sides. end of question.;)

How so? Perhaps all there is to space, to the question of "Where?", but there could be other things...all there is to what?

To assume that time is 'the' 4th dimension, you have to assume that the first three are the three we regularly encounter, and that there is no other '4th dimension'....

Hmm, but what of the other secondary color, Green?

It will colonize the moon, I tell you!

It's like trying to climb into a three-dimensional box, that you just drew on a sheet of paper...
Yeah, I remember that. I somehow woke up in a hospital afterwards.

a formula for finding out what the angle of each internal angle for a certain polygon is
(n-2)180=a
where 'n' equals the sides of the polygon and 'a' equals the internal angle toal of the polygon.
example: a triangle has 3 sides
(1-2)180=a
(1)180=a
a=180
and it's correct, triangles have a total of 180 degrees
we know circles have 360 degrees, and this is where it gets interesting
(n-2)180=360
(n-2)=2
n=4
soo, circles have 4 sides?
you could say that each degree corresponds to each internal angle, so it would have 360, but this is too small to be truly a smoth, fluent circle. you would have to divide up each angle and multiple by some infinite integer to be smooth, because even a polygon with 475948754983759834 sides is still truly not a circle.
math says a circle has 4 sides, logic says infinite.

To assume that time is 'the' 4th dimension, you have to assume that the first three are the three we regularly encounter, and that there is no other '4th dimension'....

I guess the question is: given four coordinates (x, y, z, t), can you find any object that existed ever since the beginning of the universe?

we know circles have 360 degrees

Wrong. Circles have an infinite number of degrees. However, infinity % 360 = 0.

a side is a straight line therefore a circle has no sides. end of question.;)

http://www.maa.org/mathland/mathland_10_21.html

Look, a 'curved triangle'....

To assume that time is 'the' 4th dimension, you have to assume that the first three are the three we regularly encounter, and that there is no other '4th dimension'....

....Well....ummm....the first three....are the three we regularly encounter...Aren't they? Length Width and Depth...alll perpendicular to each other, I can move my hand through them right now if you want...And...If there's another "4th" dimension....then...Time would be the fith, I suppose. another 4th dimension, would still be something "outside" of the other three, like Time, so....there might be more than L W D and T, but...we either can't measure it (yet, perhaps) or there's another way of locating a specific object we can't fathom....

we know circles have 360 degrees, and this is where it gets interesting

We do?

Yeah, I remember that. I somehow woke up in a hospital afterwards.

Yes... we've all done it, at one time or another.... seemed like such a good idea at the time... ;)

yes, with those coordinates you can find anything, ever. the most precise way to describe something, an event, besides adjectives or whatever is its location, and time in that location. like a time spanning latitude and longitude system

yes, with those coordinates you can find anything, ever. the most precise way to describe something, an event, besides adjectives or whatever is its location, and time in that location. like a time spanning latitude and longitude system

How do you know that there isn't a 5th dimension -- one which human beings lack the capacity to "see" but exists nonetheless? Perhaps this dimension accounts for things like dark matter.

we know circles have 360 degrees


Nope... Circles have an infinite number of interior angles slightly less than pi in angle

Has anyone ever really made a "perfect" circle. Try to draw a circle, yes, it's going to look crappy, but that's the point! If we can't really make circles how do we know how many sides there are? But anyways, a perfect circle would have no sides comparable to that of a polygon. Since a circle is not a polygon and is not composed of sides that we can measure, it can be created through a limitless amount of possibilities we can't even imagine. So really... Does it really matter?

How do you know that there isn't a 5th dimension -- one which human beings lack the capacity to "see" but exists nonetheless? Perhaps this dimension accounts for things like dark matter.

Possibly...But, "accounts for things like dark matter"? As in, Dark matter is located in a different position along this 5th dimension from us, so it seems to be not completely of our world?...Cuz that would sorta make sense...

....Well....ummm....the first three....are the three we regularly encounter...Aren't they? Length Width and Depth...alll perpendicular to each other, I can move my hand through them right now if you want...And...If there's another "4th" dimension....then...Time would be the fith, I suppose. another 4th dimension, would still be something "outside" of the other three, like Time, so....there might be more than L W D and T, but...we either can't measure it (yet, perhaps) or there's another way of locating a specific object we can't fathom....

We are limited by our three-dimension perceptions, and by the limitations those perception place on our understanding.

When we were infants, we perceived in pretty much two dimensions, until we learned that things didn't just get bigger and smaller, they approached and retreated along an axis we had not conceived of before.

Now, we use our three dimension understanding to interact with (what we assume is) a three dimensional reality.

But, maybe we just haven't learned to 'see' interactions on a fourth dimensional plane?... Or, maybe we have learned, but fourth-dimensional interactions can't intrude on our three-dimensional space in any 'rational' way? (A 4-D cube, intersecting 3-D space, would appear to be what we know as a 'cube'... we'd only perceive three of it's dimensional factors).

So... time... is it a fourth dimension? A fifth? A tenth?

I'm not convinced it actually drops into that organisation at all...because I don't see it intersecting that 'geometry'... but it's a handy way to describe it, I guess.

How do you know that there isn't a 5th dimension


In da maths there are an infinite number of dimensions. Finding the gradients of said dimensions can be tons-o-fun

yes, with those coordinates you can find anything, ever. the most precise way to describe something, an event, besides adjectives or whatever is its location, and time in that location. like a time spanning latitude and longitude system

Assuming only three dimensions...

Nope... Circles have an infinite number of interior angles slightly less than pi in angle

Nope, circles have an infinite number of interior angles which are infintesimally less than 180 in angle.

Possibly...But, "accounts for things like dark matter"? As in, Dark matter is located in a different position along this 5th dimension from us, so it seems to be not completely of our world?...Cuz that would sorta make sense...

Something like that, yeah. I don't know much about this stuff, though.

Novice'] If we can't really make circles how do we know how many sides there are?
That's the cool part about maths. We don't know. We define.
So really... Does it really matter?
No. That's why we discuss it in General.

We are limited by our three-dimension perceptions, and by the limitations those perception place on our understanding.

When we were infants, we perceived in pretty much two dimensions, until we learned that things didn't just get bigger and smaller, they approached and retreated along an axis we had not conceived of before.

Now, we use our three dimension understanding to interact with (what we assume is) a three dimensional reality.

But, maybe we just haven't learned to 'see' interactions on a fourth dimensional plane?... Or, maybe we have learned, but fourth-dimensional interactions can't intrude on our three-dimensional space in any 'rational' way? (A 4-D cube, intersecting 3-D space, would appear to be what we know as a 'cube'... we'd only perceive three of it's dimensional factors).

So... time... is it a fourth dimension? A fifth? A tenth?

I'm not convinced it actually drops into that organisation at all...because I don't see it intersecting that 'geometry'... but it's a handy way to describe it, I guess.

Well there's probably no actual counting order of dimensions, 1st, 2nd, 3rd, etc. dimensions is rather arbitrary....And anything that exsts has to be at least 4 dimensional.....really, it has to have some value in every dimension to exist as more than a concept, so far we know of 4 ways it must be...measureable...Technically we only percive consectutive 3 dimensional cross sections of the fourth dimension...Time doesn't really fall into geometry, I'd suppose geometry generally sticks with our three dimensions of space, perhaps adding a figurative 4th dimension of space, calling said figure a hyper cube, and asking you to get the hyper-volume. (I'd figure that still possible, but with time instead of another space dimension, an object, 4 spatial units long, 3 su wide, 5 su deep, and 2 time units...[I can't think of the right word here, long? period of existence? What word could be used there?]. Do the same thing you do with area and voulume, l*w*d*t= H[hyper volume, for lack of a better term])

Eh, rambles....


I suppose it's rather weird to see mentally, but meh....

Eh, rambles....

I suppose it's rather weird to see mentally, but meh....
With weird equalling impossible, yes? Which would be a thesis I don't support.

Nope, circles have an infinite number of interior angles which are infintesimally less than 180 in angle.

I like pi... It tastes better, and aparently my definition of slightly is smaller than yours. :D

Naw, it has two sides - an inside, and an outside.

With weird equalling impossible, yes? Which would be a thesis I don't support.

Not really, It works fine for me...But my mind is rather weird, so it makes sense I could see something as odd....

Naw, it has two sides - an inside, and an outside.

And squares don't have 2 or 8 sides because?

Assuming only three dimensions...

Well, three dimensions of space, which alone are not enough to locate something. If you know where (let's say, latitude, longitude, altitude) AND when, you could locate it, as far as we can fathom at the moment.

2: inside outside, unless its solid then there's only outside.

By that definition, a triangle would have six sides.

A circle has one side.


Actually, it would only have 2 still; all the space inside the two-dimensional figure, and all the space outside the two-dimensional figure, just like the circle.

Whitetrash Manor

And squares don't have 2 or 8 sides because?
The question-at-hand was about circles, not squares; I maintain my answer is correct - there are two sides.

The question-at-hand was about circles, not squares; I maintain my answer is correct - there are two sides.

Well then, how is that? Explain, please.

Actually, it would only have 2 still; all the space inside the two-dimensional figure, and all the space outside the two-dimensional figure, just like the circle.

Whitetrash Manor

Eh? Space isn't a side....

Actually, it would only have 2 still; all the space inside the two-dimensional figure, and all the space outside the two-dimensional figure, just like the circle.

Whitetrash Manor

By this definition all 2D polygons only have two sides. Not a useful defilition in this context. Now if you are trying to bound a problem this may be a useful definition.

edit: BTW... I think you mean area vise space

When the number of sides on a regular polygon approaches infinity it approaches a circle.

A side in the traditional sense is a straight line segment. Whereas a circle is one curve, two different things.

So either 0, 1, or infinity.

When the number of sides on a regular polygon approaches infinity it approaches a circle.

A side in the traditional sense is a straight line segment. Whereas a circle is one curve, two different things.

So either 0, 1, or infinity.

Well, what's a curve? Could it be an infinite number of infintessimal linsegemts, with angles between them infintesimally smaller than 180 degrees? (I like that word...infintesimal....hehe...)

So either 0, 1, or infinity.

The formula for calculating the angle of a polygon based on the number of sides is 180 - ( 360 / s ), with s being the number of sides. The only number that s can be for that equation to work with a circle is infinity. I really don't get how you can say that a circle has one side (a side can't be curved) or 0 sides (wtf).

Infinite.

Circles a primarily a concept of geometry, and thusly can have infinite sides as they only truly exist in the human mind.

Well, what's a curve? Could it be an infinite number of infintessimal linsegemts, with angles between them infintesimally smaller than 180 degrees? (I like that word...infintesimal....hehe...)
You could think of it that way or you can think of a circle as the set of all points a certain distance from a point. There are multiple definitions of a circle, multiple ways of achieving it.

The question of the number of sides is primarily one of interpretation.

I've always wondered about this. Is it a one sided figure? I've also heard that it's a figure of infinite sides.

2: Front and back. The perimeter can't be considered a "side" be cause no two points on the perimeter can make a line without excluding a third point in between them (it won't be in the same plane). Neither of the two possible answers you named will fit the bill; the question is in error.

(For that reason, circles are impossible to draw accurately, and we can only approximate by drawing 60000-sided polygons or so.) It isn't possible to accurately draw a circle using a compass?

Well, I don't have to:

http://www.googlefight.com/index.php...e&word2=purple

Orange is clearly more common than purple, thus it fits the answer of the question "What is the most commonly known word that does not ryhme with anything?"Well, if you're going to use that criteria, then month slaughters orange.

http://www.googlefight.com/index.php?lang=en_GB&word1=orange&word2=month

Infinite - no one can draw the "perfect circle" probably because even with the best computers, it will have say 1000,000,000 sides.

It isn't possible to accurately draw a circle using a compass?


No. It is possible to approximate one quite well, though.


Well, if you're going to use that criteria, then month slaughters orange.


The whole 'orange' debate has to be one of (the most surreal) my favourite 'thread-jacks' of all time... :)

I think it's usually taught that a circle has one side, but now that I think about it, the infinite points on a circle would make an infinite amount of sides. Boggles the mind, doesn't it? They should get the world's mathematicians on this instead of pi.

*Gasp* What if pi leads to the answer of how many sides a circle has?
pi is the way to find it, Pi-r squared, ever heard of that? Pi and a circle are pretty much the same thing, but pi is a number, and a circle is a shape

A circle does not have infinate sides, it does eventually go all the way around in 360 degrees, but depending on how it is drawn, or computer desinged (then depending on the graphics) it can have a few sides, like 20, or 100,000,000,000,000, but either way, it cannot be infinate. It is damn close though.

A circle does not have infinate sides, it does eventually go all the way around in 360 degrees, but depending on how it is drawn, or computer desinged (then depending on the graphics) it can have a few sides, like 20, or 100,000,000,000,000, but either way, it cannot be infinate. It is damn close though.

No, no... you are confusing 'approximation' for the thing, itself.

A computer has a minimum render detail it can achieve... any circle we physically construct, has a minimal level at which the 'circularity' of the thing becomes less than the margin of differentiation of the medium...

But those things are just approximations of 'a circle'.

It isn't possible to accurately draw a circle using a compass?
No, it isn't. You will instead end up drawing a multi-sided polygon very similar to a circle.

I think you've actually just proved that circles do not exist!
Correct. A circle is defined as the locus of all points equidistant from a certain point. As a point has no size, it cannot act as a "side"; sides by definition have a size. Therefore, it is simply an infinite number of points. This may seem like a paradox, but remember that 0 (the mass of a point) x 1/0 (infinity or aleph-zero) = 1, by the multiplication of reciprocals theorem.

Circles a primarily a concept of geometry, and thusly can have infinite sides as they only truly exist in the human mind.

And in the hearts of children.