# Length of bases in Polar coordinates

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## Main Question or Discussion Point

According to this video the length of basis
is r. It grows as we further from the origin . Why?

## Answers and Replies

mfb
Mentor
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.

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
Mentor
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.