Length of bases in Polar coordinates

[smodak]

According to this video the length of basis

is r. It grows as we further from the origin . Why?

 

[mfb]

There is not really a "length" of it, but you can consider how far you move if you move by a small $\epsilon \hat \theta$, the length increases with the radius.

 

[smodak]

There is not really a "length" of it, but you can consider how far you move if you move by a small $\epsilon \hat \theta$, the length increases with the radius.

Thanks. That makes sense. But why would the 'length' be r as Pavel Grinfeld says in the video.

 

[mfb]

Set $\epsilon=1$. With 2 pi you get a length of 2 pi r, with 1 you would expect a length of r. Sort of.