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Is a perfect circle possible?

  1. Jul 4, 2015 #1
    Since pi is irrational does that mean that a perfect circle could never be produced?
    Wouldn't a circle be like limit where the ratio of diameter to circumference approaches pi the radius should be the same in any direction.
     
  2. jcsd
  3. Jul 4, 2015 #2
    Or the other way around
     
  4. Jul 4, 2015 #3
    You are aware that materials are made of atoms and molecules, correct. In such a framework, is it possible to have a perfect anything?

    Chet
     
  5. Jul 4, 2015 #4
    Um no,
    But a circle must be defined by limits while lines do not
     
  6. Jul 4, 2015 #5

    mathman

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    A perfect circle or straight line or any other geometric shape is a mathematical abstraction. Physically these can't be constructed, although we can make good approximations.
     
  7. Jul 4, 2015 #6
    Agreed in a world with atoms and molecules, but the area of a circle is a limit where as area for polygons are not
     
  8. Jul 4, 2015 #7

    phinds

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    What does that have to do with whether or not you can have a perfect circle? A circle is a line. Do you think perfect lines are possible in a world of quantized "stuff" ?
     
  9. Jul 4, 2015 #8
    A circle of radius r is all of the points that lie a distance r from some partucular point. There is no need for limits.
     
  10. Jul 4, 2015 #9

    DaveC426913

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    +1 for DrewD. The collection of all points in a plane that are the same distance from a central point is a perfect circle. QED.
     
  11. Jul 5, 2015 #10

    micromass

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    You cannot have perfect circles in reality. Neither can you have perfect lines or perfect triangles. This is not only because the world consists of molecules, but also because the universe is curved. So we will never be able to create a perfect Euclidean circle since our world is not Euclidean.
     
  12. Jul 5, 2015 #11

    phinds

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    But wait. I agree that "straight" lines in our universe are not Euclidean straight lines but I thought it was possible to chose a position such that a circle IS a Euclidean circle.

    Since I'm basing this on my understanding of the Reimann geometry surface used in pop science to "picture" a black hole's effect on space-time, I certainly could be wrong, but if you look at that surface (trumpet shaped) you can see that nowhere on it could you construct a Euclidean straight line, but there IS a way, by circumscribing the "horn", to draw a line that would be a Euclidean circle.
     
  13. Jul 5, 2015 #12

    micromass

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    Do you mean that the embedding of the set in the ambient space would be a circle in the ambient space? If not, you'll need to include a picture.
     
  14. Jul 5, 2015 #13

    phinds

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    I have no idea what that means. Here's a pic with a circle shown in blue

    bh.jpg
     
  15. Jul 5, 2015 #14

    micromass

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    The area of that circle is not really ##\pi r^2##. Neither is the length ##2\pi r##. So I don't know if you can call that a Euclidean circle. It certainly is a Euclidean circle in the ambient space. But people living on the manifold will not find this circle very Euclidean. Besides, there is no ambient space in GR.
     
  16. Jul 5, 2015 #15

    phinds

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    OK. I don't follow that technically, but I believe you. Thanks.
     
  17. Jul 5, 2015 #16
    That thing looks like an ordinary circle in the ambient euclidean space it is embedded. What you're saying is very strange, i.e. it makes no sense to me.
     
  18. Jul 5, 2015 #17

    phinds

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    Quite possibly that's because, mathematically, I don't know what I'm talking about :smile: (see my previous post).
     
  19. Jul 5, 2015 #18
    You're thinking about an ambient space. Are you familiar with the fact that spacetime does not naturally live in any ambient space as far as we can tell? It's justa basic GR thing, you dont need a lot of math for that.
     
  20. Jul 5, 2015 #19

    micromass

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    Don't believe me just like that. Here's a question: on the figure you linked, can you show me what the center and the radius of the circle is?
     
  21. Jul 5, 2015 #20

    WWGD

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    Maybe we could use the area form (of the universe, given the assumptions) to add to Micromass' argument about the area and diameter of the circle.
     
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