I Length of bases in Polar coordinates

smodak
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According to this video the length of basis
Inline57.gif
is r. It grows as we further from the origin . Why?
 
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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.
 
mfb said:
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.
 
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.
 
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