What is the direction of a rotation?
We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.
For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?
We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.
geometry rotations orientation
asked Nov 29 '18 at 13:32
SephiSephi
1056
add a comment |
We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.
For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?
We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.
geometry rotations orientation
asked Nov 29 '18 at 13:32
SephiSephi
1056
add a comment |
We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.
For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?
We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.
geometry rotations orientation
asked Nov 29 '18 at 13:32
SephiSephi
1056
We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.
For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?
We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.
geometry rotations orientation
geometry rotations orientation
asked Nov 29 '18 at 13:32
SephiSephi
1056
asked Nov 29 '18 at 13:32
SephiSephi
1056
asked Nov 29 '18 at 13:32
SephiSephi
1056
asked Nov 29 '18 at 13:32
SephiSephi
1056
asked Nov 29 '18 at 13:32
SephiSephi
1056
1056
add a comment |
add a comment |
1 Answer
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An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
add a comment |
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1 Answer
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1 Answer
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active
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An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
add a comment |
An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
add a comment |
An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
An instantaneous rotation and a continuous rotation are two different things. An instantaneous rotation has no direction. It has a before and after, and that's it.
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
answered Nov 29 '18 at 13:43
ArthurArthur
111k7107189
111k7107189
add a comment |
add a comment |
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