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Why is a cylinder not perfectly symmetric as a sphere?

1

$begingroup$

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

share|cite|improve this question

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 | 

1

$begingroup$

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

share|cite|improve this question

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

share|cite|improve this question

asked Mar 31 at 6:38

veronikaveronika

28111

$endgroup$

share|cite|improve this question

asked Mar 31 at 6:38

veronikaveronika

28111

share|cite|improve this question

asked Mar 31 at 6:38

veronikaveronika

28111

asked Mar 31 at 6:38

veronikaveronika

28111

asked Mar 31 at 6:38

veronikaveronika

28111

1 Answer
1

active

oldest

votes

4

$begingroup$

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.

share|cite|improve this answer

answered Mar 31 at 13:04

Dac0Dac0

6,0671937

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4

$begingroup$

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.

share|cite|improve this answer

answered Mar 31 at 13:04

Dac0Dac0

6,0671937

$endgroup$

add a comment | 

4

$begingroup$

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.

share|cite|improve this answer

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.

share|cite|improve this answer

answered Mar 31 at 13:04

Dac0Dac0

6,0671937

$endgroup$

share|cite|improve this answer

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