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Paradox: Circular Rooms and Corners

Discussion in 'Off-Topic' started by giantpinkbunnyhead, Mar 23, 2004.

  1. giantpinkbunnyhead

    giantpinkbunnyhead IncGamers Member

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    Paradox: Circular Rooms and Corners

    I don't know why this popped into my head, but it did and so now I'm going to put it in all of your heads too.

    Does a perfectly circlular room have NO corners; or INFINITE corners?

    Of course, first we have to define "corner". Is being 90 degrees a requirement? Would a 1 degree angle constitute a corner? After all, two straight lines come together at an angle. A shallow angle but still an angle. Then, if 1 degree works, what about 0.000002 degrees? Couldn't a circle possibly be a bazillion shallow corners between a bazillion sides, that as the number approaches infinity the shape looks more and more like the perfect circle?

    OR.....

    Would a truly perfect circular room actually be curved on the smallest, most infinitely small microscopic level, thereby having no straight segments with which to form a corner? This flies in the face of the notion that all curves are merely a large number of small, straight segments joined by a large number of extremely shallow angles.

    What do you think?
     
  2. AeroJonesy

    AeroJonesy IncGamers Member

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    edit: see below
     
  3. toader

    toader Banned

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    I understand what your saying.

    If your talking about a real life constructed circle room, then yes, it will have tons of tiny corners.

    But if your talking about a theoretically perfect circular room, then no, there is no corners at all, no matter how close you look on the line of the circle.
     
  4. Suicidal Zebra

    Suicidal Zebra IncGamers Member

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    I ascribe to neither philosophy.

    In reality, a truely curved room would have no corners, but an large number of atom sized dimples. :D
     
  5. AeroJonesy

    AeroJonesy IncGamers Member

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    Does .9999... = 1?

    I'd imagine this is the same sort of question here.

    My guess is that a circle has zero corners, because it is perfectly curved. So there are no straight segments. If you look at the equation for a circle, it has an x^2 term in it. The derivative of that is 2x which means that the derivative is never a straight line, so there's no straight lines on a circle. Just my guess though.
     
  6. toader

    toader Banned

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    Again...same thing.

    If your talking real life, then there has to be some sort of significant digit to stop at depending on your measuring device. If your device can measure 6 digits then 0.99999 = 0.99999 and 0.999999 = 1.

    If your talking theory, then no, 0.999999999999(cont) doesnt equal 1.
     
  7. giantpinkbunnyhead

    giantpinkbunnyhead IncGamers Member

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    Yeah, this is PURELY theoretical... assuming this room existed, it would be built perfectly with no error in measurement or construction. This is getting down to the finest level of detail... is a truly curved surface really "curved", or is a curve simply an infinite number of infinitely small segments joined together? As AeroJonesy said, it's like the .999 =1 thing. They both can be argued to make sense.
     
  8. bigD72

    bigD72 IncGamers Member

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    Negligible amount.

    Say you have a choice of 1 full candy bar (=1) or another candy bar that is equal to .9999(cont) that amount is so negligble it doesn't matter which you choose, but thats real life application not theory.
     
  9. P2blr

    P2blr IncGamers Member

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    a CIRCULAR room would of course have corners.

    depending on which side you are on, it would either have 2 sides or infinity + 2 sides, because of the roof and floor, assuming that there is a door that fits perfectly in sync with it.

    Now, if you are talking about a SPHERICAL room, now that's different, could have just asked if a ball or perfect sphere had corners.

    Although I personally subscribe to the "no corner" team for now
     
  10. Wuhan_Clan

    Wuhan_Clan IncGamers Member

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    This is one of the concepts used to calculate pi. A polygon with say 8 sides (like a stopsign) doesn't look much like a circle. What about 20 sides? A polygon with 100 sides look reasonably like a circle without fine detail. So as the number of sides to a polygon tends to infinity, the polygon becomes a circle. (and so the more sides you have, the more accurately you can calculate pi).

    So theoretically, the infinitely-sided polygon never quite becomes an actual circle. Theoretically then, the circle doesn't have corners. Of course practically, we can't construct perfect circles.
     
  11. Freemason

    Freemason Banned

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    Time to muck things up. I believe a perfectly sphereical room would be nothing but corners. Seeing as how space is curved, and bending a curved line diametrically opposite of it's origional shape makes it straight, a spherical room can be nothing but a box.
     
  12. Deadbolt'd

    Deadbolt'd IncGamers Member

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    Dictionary.com says-

    The position at which two lines, surfaces, or edges meet and form an angle: the four corners of a rectangle.
    The area enclosed or bounded by an angle formed in this manner: sat by myself in the corner; the corner of one's eye.
    The place where two roads or streets join or intersect.

    That would depend on your definition of "perfect circle." Would "perfect circle" mean that it has no angles and is made of 1 line? If there actually WERE infinite corners to a (perfectly) circular room, then it would not work for that idea of "perfect," but how could you tell? It would be, as you said, a perfect circle.
    How much did I miss, or how off am I? I'm sure there's something I havn't thought of.

    -DB
     
  13. Wuhan_Clan

    Wuhan_Clan IncGamers Member

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    Perhaps ... if our circle or sphere had mass.
    Anyways, there is no need to talk about circles in more then 2 dimensions since we can never see it in anything else. But even if space is curved, how do you know the curvature will transform the cirlce into a polygon? If you drew a circle on a piece of paper and then you curled the paper into a ball shape, 2 dimensionally from our perspective, it looks like an ellipse (also with no corners).
     
  14. Freemason

    Freemason Banned

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    The curvature of space is dependant upon how much gravitational force is applied to it. So there is no way to know for certain how much space would curve a sphere.
     
  15. publius

    publius IncGamers Member

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    Perhaps another point of view (taken from one of the ways to calculate pi): Consider a regular polygon. As you add more and more sides to it, the polygon looks more and more like a circle.
     
  16. Wuhan_Clan

    Wuhan_Clan IncGamers Member

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    The problem with describing the percfect circle comes from the ideas of infinity. The perfect circle can only be described as a polygon with infinitly many sides. Therefore, the angle that 2 sides make would be infinitly small (whatever infinity means). The reason you have to describe it in this way is that if there never is an internal angle, how do you get curvature?

    The real question is what do we mean by something being infinitly many or infinitly small? Our common sense doesn't allow us to comprehend such concepts so its difficult for us to discuss whether its possible or not. Afterall, its existence can only be described as much as what our brains can comprehend.


    As for the curvature of a circle in space-time, I don't know the math behind relativity to know how things work.
     
  17. Stevinator

    Stevinator IncGamers Member

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    okay my BS detector went off, and it pointed me here....

    if oyu are bending a curved line youdon't necessarily get a straight line...in fact getting a straight line is terribly unlikely. you could get more curved lines, oyu could get lines that curve both directions...you could get tons of different shapes...but the person in the room would still see a circular room, and the circular room has two corners. one around the floor and one around the ceiling.
    Circular rooms make cylinders. and if the right angle of a rectangle can be a corner, then the right angle in our room can be a corner.

    the real question is how much would you have to pay for a curved piece of molding that comes back and touches itself? there'd be no good place to hook it back together...you couldn't us flex, and you'd have to build the room around the base and crown molding!!! what a nightmare!!!
     
  18. caddad

    caddad IncGamers Member

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    Coming from a design engineering background I would say absolutely.

    A room by definition needs an entry point and has to have walls of a certain depth, even miniscule.

    A circular room by definition is cylindrical, therefore having a flat or angled ceiling and a flat floor. Where the circular wall meets the floor or ceiling, regardless of angle, it would in fact make a corner. (think silhouette edge in plan view.)

    If you are speaking of a spherical room then the only corners would be where the door was made. (even a round door has to have depth, therefore corners)

    -D2netDad
     
  19. rodigee

    rodigee IncGamers Member

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    <stupid idea>
    Is it possible that the entire room itself could be just one abstract 360 degree "corner"?
    </stupid idea>
     
  20. Wuhan_Clan

    Wuhan_Clan IncGamers Member

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    Correct except you wouldn't have a room. You just have all of space. (its like having a pole of which the diameter is a singularity and the "room" is all the space around it)
     

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