Why is a cylinder not perfectly symmetric as a sphere? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How do I figure out the speed of a jet of water in this example?Just a thought… defining “competition”?Why is volume of cylinder > volume of cubeHow to discover the dimensions of a sphere, from specific dimensions of a cylinder?Sphere inside cylinder vs polyhedra?Smallest enclosing cylinderWhy do we use “If p,then q” instead of “Not p or q”?Why this integral does not work to calculate Cut Cone Volume?Constraints of $n$-dimensional cylinder inside sphereCutting out a cylinder of maximum possibe size from a cube
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Why is a cylinder not perfectly symmetric as a sphere?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How do I figure out the speed of a jet of water in this example?Just a thought… defining “competition”?Why is volume of cylinder > volume of cubeHow to discover the dimensions of a sphere, from specific dimensions of a cylinder?Sphere inside cylinder vs polyhedra?Smallest enclosing cylinderWhy do we use “If p,then q” instead of “Not p or q”?Why this integral does not work to calculate Cut Cone Volume?Constraints of $n$-dimensional cylinder inside sphereCutting out a cylinder of maximum possibe size from a cube
$begingroup$
I have read that a cylinder not being perfectly symmetric is the reason behind Rayleigh instability: the process that makes bubbles out of a stream of water.
But a cylinder seems also perfectly symmetric to me
geometry soft-question physics
asked Mar 31 at 6:38
veronikaveronika
28111
$endgroup$
add a comment |
$begingroup$
I have read that a cylinder not being perfectly symmetric is the reason behind Rayleigh instability: the process that makes bubbles out of a stream of water.
But a cylinder seems also perfectly symmetric to me
geometry soft-question physics
asked Mar 31 at 6:38
veronikaveronika
28111
$endgroup$
2
$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34
add a comment |
$begingroup$
I have read that a cylinder not being perfectly symmetric is the reason behind Rayleigh instability: the process that makes bubbles out of a stream of water.
But a cylinder seems also perfectly symmetric to me
geometry soft-question physics
asked Mar 31 at 6:38
veronikaveronika
28111
$endgroup$
I have read that a cylinder not being perfectly symmetric is the reason behind Rayleigh instability: the process that makes bubbles out of a stream of water.
But a cylinder seems also perfectly symmetric to me
geometry soft-question physics
geometry soft-question physics
asked Mar 31 at 6:38
veronikaveronika
28111
asked Mar 31 at 6:38
veronikaveronika
28111
asked Mar 31 at 6:38
veronikaveronika
28111
asked Mar 31 at 6:38
veronikaveronika
28111
asked Mar 31 at 6:38
veronikaveronika
28111
28111
2
$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34
add a comment |
2
$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34
2
2
$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34
add a comment |
1 Answer
1
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$begingroup$
Suppose to have a sphere of crystal. You can rotate the sphere in every direction and it will always look the same and you will never be able to tell if it's up or down (the question doesn't even make sense). Instead take a crystal glass with the shape of a cylinder. You will always be able to tell if the glass is standing up or laying down on the table.
This is because you can switch the axis $x,y,z$ and the sphere will appear always the same, while with the cylinder you will always have an axis which is different from the other two.
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
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add a comment |
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$begingroup$
Suppose to have a sphere of crystal. You can rotate the sphere in every direction and it will always look the same and you will never be able to tell if it's up or down (the question doesn't even make sense). Instead take a crystal glass with the shape of a cylinder. You will always be able to tell if the glass is standing up or laying down on the table.
This is because you can switch the axis $x,y,z$ and the sphere will appear always the same, while with the cylinder you will always have an axis which is different from the other two.
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
$endgroup$
add a comment |
$begingroup$
Suppose to have a sphere of crystal. You can rotate the sphere in every direction and it will always look the same and you will never be able to tell if it's up or down (the question doesn't even make sense). Instead take a crystal glass with the shape of a cylinder. You will always be able to tell if the glass is standing up or laying down on the table.
This is because you can switch the axis $x,y,z$ and the sphere will appear always the same, while with the cylinder you will always have an axis which is different from the other two.
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
$endgroup$
add a comment |
$begingroup$
Suppose to have a sphere of crystal. You can rotate the sphere in every direction and it will always look the same and you will never be able to tell if it's up or down (the question doesn't even make sense). Instead take a crystal glass with the shape of a cylinder. You will always be able to tell if the glass is standing up or laying down on the table.
This is because you can switch the axis $x,y,z$ and the sphere will appear always the same, while with the cylinder you will always have an axis which is different from the other two.
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
$endgroup$
Suppose to have a sphere of crystal. You can rotate the sphere in every direction and it will always look the same and you will never be able to tell if it's up or down (the question doesn't even make sense). Instead take a crystal glass with the shape of a cylinder. You will always be able to tell if the glass is standing up or laying down on the table.
This is because you can switch the axis $x,y,z$ and the sphere will appear always the same, while with the cylinder you will always have an axis which is different from the other two.
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
answered Mar 31 at 13:04
Dac0Dac0
6,0671937
6,0671937
add a comment |
add a comment |
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$begingroup$
The symmetry group of a sphere is a Lie group of dimension $3$. The symmetry group of a cylinder is a Lie group of dimension $1$.
$endgroup$
– Lord Shark the Unknown
Mar 31 at 6:47
$begingroup$
(Or dimension $2$, if one means a [doubly] infinite cylinder.)
$endgroup$
– Travis
Mar 31 at 7:06
$begingroup$
Also, that seems as good of an explanation as one could hope for. Perhaps write it up as an answer proper?
$endgroup$
– Travis
Mar 31 at 7:07
$begingroup$
@Travis Can you explain this?
$endgroup$
– veronika
Mar 31 at 8:09
$begingroup$
Sure: By a doubly infinite cylinder, I just mean a cylinder that extends infinitely far in both directions. Concretely, consider $(x, y, z) in Bbb R^3 : x^2 + y^2 = 1$, which is a cylinder of radius $1$ with symmetry axis the $z$-axis. Its symmetry group has dimension two, or, roughly speaking, there are two independent ways to move the cylinder without changing its appearance: One can slide it parallel to its axis of symmetry, or one can rotate it along that axis. If the cylinder is finite (or infinite in only one direction), only rotations are symmetries.
$endgroup$
– Travis
Apr 1 at 2:34