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Math Help - Why would you ever need/want r to be negative in polar coordinates?

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    Why would you ever need/want r to be negative in polar coordinates?

    In polar coordinates, if you only allow r to be positive, you can always use the appropriate angle to still get the same point you would have gotten by using a negative value of r and a theta that differs by 180 degrees.
    So why is there not a convention to just only allow positive r? Is it because equations of curves are harder to write if one does not allow r to be negative?
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    Re: Why would you ever need/want r to be negative in polar coordinates?

    Quote Originally Posted by lamp23 View Post
    In polar coordinates, if you only allow r to be positive, you can always use the appropriate angle to still get the same point you would have gotten by using a negative value of r and a theta that differs by 180 degrees.
    So why is there not a convention to just only allow positive r? Is it because equations of curves are harder to write if one does not allow r to be negative?
    It is a matter of history.
    Although there are solid mathematical reasons for doing it that way.
    In exponential form z=|z|\exp(i\cdot\text{Arg}(z)).
    So there r=|z| which is a non-negative number.
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