- #1
smodak
- 457
- 252
According to this video the length of basis
Length of bases in Polar coordinates
- Context: Undergrad
- Thread starter smodak
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the concept of the length of bases in polar coordinates, exploring how this length behaves as one moves away from the origin. Participants examine the implications of this behavior in both theoretical and practical contexts.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification
Main Points Raised
- Some participants suggest that the length of the basis in polar coordinates is represented by the radius, r, and that it increases as one moves away from the origin.
- Others argue that the concept of "length" may not be straightforward, proposing that one should consider the distance moved when changing the angle by a small amount, ##\epsilon \hat \theta##, which also suggests that the length increases with the radius.
- A later reply questions the assertion made in a referenced video by Pavel Grinfeld, seeking clarification on why the length is stated to be r.
- Another participant proposes a specific case by setting ##\epsilon=1##, indicating that with a full rotation (2 pi), the length would be 2 pi r, while a smaller increment would yield a length of r, though this is presented as a somewhat tentative conclusion.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the definition and implications of "length" in polar coordinates, with multiple competing views and interpretations remaining in the discussion.
Contextual Notes
Limitations include the ambiguity surrounding the term "length" and its dependence on the context of movement in polar coordinates, as well as unresolved mathematical steps in the reasoning presented.
According to this video the length of basis
- #2
mfb
Mentor
- 37,449
- 14,315
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.
- #3
smodak
- 457
- 252
Thanks. That makes sense. But why would the 'length' be r as Pavel Grinfeld says in the video.mfb said:
- #4
mfb
Mentor
- 37,449
- 14,315
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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