Thread: Negative radius

I have just been informed (and been able to verify on the web) that the polar coordinate system allows the use of r < 0.

I was never taught that. When did this convention start being used? Did my teachers simply not happen to use it?

-Dan

Originally Posted by topsquark

I have just been informed (and been able to verify on the web) that the polar coordinate system allows the use of r < 0.

I was never taught that. When did this convention start being used? Did my teachers simply not happen to use it?

-Dan

"The r is normally limited to non-negative numbers, but negative r is sometimes used to represent a point at an angle pi apart from the theta specified."

from polar coordinates@Everything2.com

Originally Posted by topsquark

I have just been informed (and been able to verify on the web) that the polar coordinate system allows the use of r < 0.

I was never taught that. When did this convention start being used? Did my teachers simply not happen to use it?

-Dan

You need the idea of a negative value for r when drawing graphs of things like $\displaystyle r = 1 - 2 \sin \theta$. For this example, when $\displaystyle \theta = \frac{\pi}{2}$ you get r = -1. The corresponding Cartesian coordinates of [-1, pi/2] are (0, -1).