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Thread: Does a circle have one side or an infinite number of sides?

  1. #1 Does a circle have one side or an infinite number of sides? 
    Forum Freshman Deaths_Child's Avatar
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    My math homework made me think of this and i want someone elses take on the issue.


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  3. #2 Re: Does a circle have one side or an infinite number of sid 
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    Perhaps this depends on the branch of mathematics that you are considering. Under normal circumstances, ie geometry, a circle is considered to have one side.


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  4. #3  
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    Moreover, it fully depends on how you define the term "side".
    I doubt that there is a strict definition of this term in mathematics. It's like talking about points.
    As Euclid defined: "A points is something that has no parts"...and ran directly into difficulties, since the term "part" remains undefined.
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  5. #4  
    Forum Radioactive Isotope cosmictraveler's Avatar
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    Actually a circle has two sides, the inside and the outside!
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  6. #5  
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    Well if you have a 2D representation of a circle then it has 3 sides. Inside, Outside and Front side. The back side is still in debate
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  7. #6 Re: Does a circle have one side or an infinite number of sid 
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    Quote Originally Posted by Deaths_Child
    Does a circle have one side or an infinite number of sides? My math homework made me think of this and i want someone else's take on the issue.
    Good question! It seems as though you are referring to the notion that a circle can be thought of as a polygon with an infinite number of sides, each of infinitesimal length.
    When we do calculus, this is assumed by the notion of taking limits for tangents of any curve.

    So, your answer is, an infinity of sides, though it might not be wise to think too literally along these lines.
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  8. #7 Agreed 
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    I agree with the symplectic that it depends that how u define a side.................like as far as i think a circle has 360 sides.........b/c i consider a side=1 degree...........if u define the side as a point than a circle has infinite sides as said by guitarist.
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  9. #8 Re: Agreed 
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    Quote Originally Posted by Latent.sage
    if u define the side as a point than a circle has infinite sides as said by guitarist.
    I do not agree. A point is not a meaningful word, such that it has no value. If by point you mean a geometric point, as you seem to have assumed, then you should make that clear.
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  10. #9 Re: Agreed 
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    Quote Originally Posted by Latent.sage
    if u define the side as a point than a circle has infinite sides as said by guitarist.
    Except |I never said that that! I said the circle can be thought of (abstractly, of course) as a polygon of infinitely many, infinitesimal sides. Not points, that's another matter (like point sets?)
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  11. #10 Re: Agreed 
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    Quote Originally Posted by Guitarist
    I said the circle can be thought of (abstractly, of course) as a polygon of infinitely many, infinitesimal sides. Not points, that's another matter (like point sets?)
    What would be the make up of each of these sides, if not individual points?
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  12. #11  
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    Very interesting. A continuous circular line containing all those tangents...but how about:

    "The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning.

    And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton."

    Does this mean that in physical reality the continuity is an illusion, and that the number of "real" sides is the circumference/planck length? A big number, but not infinite?
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  13. #12  
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    To have a side you need to have 3 collinear points. But circle dosenit have 3 coolinear points. Thus it has 0 sides
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  14. #13  
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    a circle is only a 360 degree angle.
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  15. #14 Sides of a circle???? 
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    Is any one fimilar with the standard form the circular equation?

    It is


    (x-x1)^2+(y-y1)^2=r^2

    This in turn yealds a two dimention entity and for sides are concerned form the definition of a two dimention is concerned it only has two sides.

    Remember

    an entitiy is two dimentional iff

    for all x which belongs to the set of real numbers and all y belongs to the set of real numbers this implies R^2 is an odered pair of (x,y).

    this two dimentional equation always yelds two sides as in term two dimention.

    For further reference consult any standard text of advanced Linear algebra.
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  16. #15  
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    a circle is really defined as the set of all points equidistant from a reference point. so I guess, I would say that it has no sides. but it does have one boundary.
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  17. #16 Re: Does a circle have one side or an infinite number of sid 
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    Quote Originally Posted by Deaths_Child
    My math homework made me think of this and i want someone elses take on the issue.
    Defining a "side" as a straight part of the perimeter of a closed loop, a circle has NO "sides". A circle is curved. It's the question that's wrong.
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