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

• Oct 12th 2011, 01:46 PM
lamp23
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?
• Oct 12th 2011, 01:58 PM
Plato
Re: Why would you ever need/want r to be negative in polar coordinates?
Quote:

Originally Posted by lamp23
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 $\displaystyle z=|z|\exp(i\cdot\text{Arg}(z))$.
So there $\displaystyle r=|z|$ which is a non-negative number.