- #1
smodak
- 459
- 253
According to this video the length of basis
Length of bases in Polar coordinates
- I
- Thread starter smodak
- Start date
In summary, the video discusses the concept of the length of basis, and explains that it grows as the distance from the origin increases. However, there is not a specific length for the basis, but rather it can be measured by how far you move with a small ##\epsilon \hat \theta##. This length also increases with the radius. Additionally, setting ##\epsilon=1## and using 2 pi as the angle, the resulting length would be 2 pi r, while with an angle of 1, the expected length would be r. This concept is explained by Pavel Grinfeld in the video.
According to this video the length of basis
- #2
mfb
Mentor
- 37,260
- 14,096
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
- 459
- 253
Thanks. That makes sense. But why would the 'length' be r as Pavel Grinfeld says in the video.mfb said:
- #4
mfb
Mentor
- 37,260
- 14,096
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.
FAQ: Length of bases in Polar coordinates
1. What are polar coordinates?
Polar coordinates are a coordinate system used to locate points in a plane using a distance from the origin and an angle.
2. How are points represented in polar coordinates?
In polar coordinates, points are represented as (r,θ) where r is the distance from the origin and θ is the angle from the reference axis.
3. What is the length of the base in polar coordinates?
The length of the base in polar coordinates is the distance from the origin to the point on the x-axis where the angle θ intersects.
4. How do you calculate the length of the base in polar coordinates?
The length of the base in polar coordinates can be calculated using the Pythagorean theorem, where the length of the base (b) is equal to r*sin(θ).
5. Can the length of the base be negative in polar coordinates?
No, the length of the base in polar coordinates is always positive, as it represents a distance from the origin.