Rationals and irrational numbers as coordinates

Discussion in 'General Math' started by Al Bundy, Feb 22, 2005.

  1. Al Bundy

    Al Bundy Guest

    In the pair (r,theta) where theta is an angle ...of course the
    irrational pi is used to describe the theta coordinate.

    If one didn't have an irrational number to describe theta.....then the
    curve fragment (s=r* theta) would not be a curved line but would be a
    series of straight lines approximating a curve. So it seems that when
    we go to two dimensions.....the irrationals have to be included in the
    domain.

    We do this and we get a basic curved surface acting as a coordinate.
    Think about how much easier some math operations would be with such a
    fundamental change. One major problem with imaginary numbers is that
    it is a rectilinear coordinate system.
     
    Al Bundy, Feb 22, 2005
    #1
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  2. Al Bundy

    Jim Spriggs Guest

    Do you mean as in 0 <= theta < 2*pi ? In what sense is pi used to
    describe the theta coordinate? How is the irrationality of pi
    relevant? One might measure angles differently and write
    0 <= theta < 360.
    In any number of dimensions one uses real numbers (rational and
    irrational) as coordinates: R, R^2, R^3, ... This isn't something that
    just happens in two dimensions with polar coordinates.
    What is "a rectilinear coordinate system"? If it's that "one major
    problem", why is it a problem? If it's the imaginary numbers, then they
    aren't a rectilinear coordinate system. Each imaginary number is a real
    number multiplied by i. i, if you like, is the ordered pair
    (0, 1), so the imaginary number iy is just (0, y) but neither it, nor
    the set of all of them, is a rectilinear coordinate system.
     
    Jim Spriggs, Feb 22, 2005
    #2
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