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Perfect Circle?

  1. Jan 30, 2004 #1
    SImple request here, I read some years ago that a perfect circle cannot be drawn freehand?..or does not exist?

    I cannot remember who said it, I belive it has some ancient meaning?

    Can anyone point me in a relevant direction?..ie who said it?
     
  2. jcsd
  3. Jan 30, 2004 #2
    probably Plato.
    All geometric figures are in your head. Outside, close enough is good enough.
     
  4. Jan 31, 2004 #3
    Thanks, I agree 100%!

    It seems that the correspondence between reality and consciousness,or imagination? can lead one to a perfect world, geometrically speaking of course!

    So, outside is just an approximation of an inner perfection? we measure things by observation, and every observation has its limitations imposed by the Observer, we are not perfect,thanks again for the handwaving towards Plato.
     
  5. Feb 1, 2004 #4
    Interesting. Why is this?
     
  6. Feb 2, 2004 #5
    It has to do with the act of abstraction.
    You cannot draw a perfect circle because you do not have a pen with zero size. You imagine the perfect circle and you can work with that.
    When it comes time to put it outside, you draw the new circle or figure.
    In the same sense, there are no numbers. There are only symbols of numbers, but that does not prevent us from working with them as if there were numbers.
     
    Last edited: Feb 2, 2004
  7. Feb 3, 2004 #6
    well, maybe on a large scale, yes -- it is impossible to create a perfect circle (or any other geometric figure).


    but what about on a small scale? on the atomic or subatomic scale?
     
  8. Feb 3, 2004 #7
    Well, no. We cannot create a perfect circle large or small. I'm pretty sure that no particles on any level are a "perfect" geometric shape (excluding their exact shape being called a "geometric shape")
     
  9. Feb 4, 2004 #8
    Ah yes. Some particles are believed to be a point. No dimension. No problem.
     
  10. Feb 4, 2004 #9
    Anything viewed from far enough away is a "point", 'no dimension' means 'NO existence' otherwise it is "one dimensional" which is the infinite/infinity (unprovable!)...as for a perfect circle, well historically speaking......
     
  11. Feb 5, 2004 #10
    heh, I know of a Calculus teacher who can draw the extremely-close-to-perfect circles w/out aid of tools. Consistent too, I dont know of anyone else like him.
     
  12. Feb 6, 2004 #11
    "No dimension" doesn't mean no existance. It only means no volume. For example leptons are believed to be dimensionless. But they have mass, spin and charge. I know this seems nonsense but the truth is this. Our experiment tools aren't perfect so we find 0.000000001 of a micron for an electron's diameter. But in theory, they're dimensionless as I said.
    But at early periods of 20th century, protons were believed to be very small (there were sense at that time). Later, they discovered that protons weren't that small. They were made up by quarks which is now believed to be a point particle. Perhaps the same will occur for leptons. No one knows.
     
  13. Feb 6, 2004 #12
    Sorta what I was trying to point out, Sorta, just in less words...(As I already knew that...)
     
  14. Feb 6, 2004 #13
    I could be wrong, and I probably am, but I thought that Ions and a few other things were naturally circles do to gravity?
     
  15. Feb 6, 2004 #14
    Actually I think that expression is something more along the lines of "Only Crazy people can draw perfect circles" probably cause only a 'crazy' person would believe they could, or had, or knew what a perfect circle looked like...

    Heck I did (drew) a "perfect circle" once, but it isn't the thought in your head now...
     
  16. Jul 1, 2004 #15
    Interesting, If gravity is constant, then the center of mass of something would complete a perfect circle right.?
    But, how could this be when we know that every thing in the 'verse acts upon each other , no matter how minute of an influence?(deviated path)
    Actually I think this is closer to a perfect circle than trying to think platonically. That is , a perfect circle would have to be "more" than a circle.
    wouldn't it need more than 3 dimensions?
     
  17. Jul 5, 2004 #16

    arivero

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    Gold Member

    The big big problem is not to draw a perfect circle, but to draw the perfect tangent to it. Or to any general curve.
     
  18. Jul 5, 2004 #17

    HallsofIvy

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    When you get down to the size of atoms and elementary particles the whole concept of "shape" is on shaky ground!

    If you take something really large, like a planet or star, then the "relative" error becomes very small and you are probably as close to a sphere (not a circle) as you can get.
     
  19. Jul 10, 2004 #18
    If any thing shaped as a circle is zoomed ... it will look like it's all pixelated which doesn't make it a circle anymore.
     
  20. Jul 10, 2004 #19
    It's a good question , but nature has the sense not to ask it , nature does not bother with static perfection such as sqr(2) , or perfect circles or pi etc. it just dithers all it's particles and makes sure that you cannot count them ( plural many).
     
  21. Jul 10, 2004 #20
    By the same token, can you find a perfect triangle? A perfect line? A perfect plane? I don't think so. Any shape is "perfect" only as an abstract concept, and the actual dimensions and magnitudes of any real-world object are known only to within some non-zero degree of inaccuracy, except where we define our units based off them.

    On the other hand, an image correctly rendered to a computer screen can be a perfect representation of some geometric figure given the limits of the display. I could graph a function by placing Go pieces on the squares of a Go board. If I did it correctly, the resulting graph would be a perfect representation of the function. It doesn't matter that the pieces will not be centered perfectly, or that the lines on the board were not drawn perfectly straight in the first place. It still conveys the same abstract concept to the observer, and that concept is perfect, even though its representation in the real world cannot be.
     
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