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A way to calculate volume of a zip-loc bag using only mathematical methods
$begingroup$
The Zip-loc challenge is pretty old, but I was doing it today to test my knowledge of chemistry. The way I calculated the volume of a ziplock bag was to fill to with water and find the calculate how much water was put in.
My Question:
Is there a purely mathematical way to calculate the volume of said ziplock bag? Two thoughts came to mind:
1) Use a Fourier series to represent the bag in a 2D coordinate system, and use axes of rotation to come up with an answer
2) Use a multivariable function to model the bag, and use a double integral to calculate volume
Would either of these methods be viable? And if they are, does it make sense to solve for an exact value rather than use the approximation when filling with water?
P.S: I'm nit really sure what SE this would belong on, but I thought since my question was mostly mathematical, this would be the right one.
Thanks in Advance!
EDIT:
For those wondering, the dimensions of the particular bag I was using is 16.5 x 14.9 cm
integration volume
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
add a comment |
$begingroup$
The Zip-loc challenge is pretty old, but I was doing it today to test my knowledge of chemistry. The way I calculated the volume of a ziplock bag was to fill to with water and find the calculate how much water was put in.
My Question:
Is there a purely mathematical way to calculate the volume of said ziplock bag? Two thoughts came to mind:
1) Use a Fourier series to represent the bag in a 2D coordinate system, and use axes of rotation to come up with an answer
2) Use a multivariable function to model the bag, and use a double integral to calculate volume
Would either of these methods be viable? And if they are, does it make sense to solve for an exact value rather than use the approximation when filling with water?
P.S: I'm nit really sure what SE this would belong on, but I thought since my question was mostly mathematical, this would be the right one.
Thanks in Advance!
EDIT:
For those wondering, the dimensions of the particular bag I was using is 16.5 x 14.9 cm
integration volume
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
1
$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38
add a comment |
$begingroup$
The Zip-loc challenge is pretty old, but I was doing it today to test my knowledge of chemistry. The way I calculated the volume of a ziplock bag was to fill to with water and find the calculate how much water was put in.
My Question:
Is there a purely mathematical way to calculate the volume of said ziplock bag? Two thoughts came to mind:
1) Use a Fourier series to represent the bag in a 2D coordinate system, and use axes of rotation to come up with an answer
2) Use a multivariable function to model the bag, and use a double integral to calculate volume
Would either of these methods be viable? And if they are, does it make sense to solve for an exact value rather than use the approximation when filling with water?
P.S: I'm nit really sure what SE this would belong on, but I thought since my question was mostly mathematical, this would be the right one.
Thanks in Advance!
EDIT:
For those wondering, the dimensions of the particular bag I was using is 16.5 x 14.9 cm
integration volume
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
$endgroup$
The Zip-loc challenge is pretty old, but I was doing it today to test my knowledge of chemistry. The way I calculated the volume of a ziplock bag was to fill to with water and find the calculate how much water was put in.
My Question:
Is there a purely mathematical way to calculate the volume of said ziplock bag? Two thoughts came to mind:
1) Use a Fourier series to represent the bag in a 2D coordinate system, and use axes of rotation to come up with an answer
2) Use a multivariable function to model the bag, and use a double integral to calculate volume
Would either of these methods be viable? And if they are, does it make sense to solve for an exact value rather than use the approximation when filling with water?
P.S: I'm nit really sure what SE this would belong on, but I thought since my question was mostly mathematical, this would be the right one.
Thanks in Advance!
EDIT:
For those wondering, the dimensions of the particular bag I was using is 16.5 x 14.9 cm
integration volume
integration volume
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
edited Jan 31 at 6:19
Aniruddh Venkatesan
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
asked Jan 31 at 6:13
Aniruddh VenkatesanAniruddh Venkatesan
151113
151113
1
$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38
add a comment |
1
$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38
1
1
$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38
add a comment |
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$begingroup$
This is a pretty hard problem even if you do not consider the elasticity of the material. Also your answer will depend heavily on how you hold or support the bag. Since I see no rotational symmetry your first approach does not make sense to me. The problem with your second approach that you don't know how the bag will deform so you don't know which function to integrate. Problems as such are typically the subject of "calculus of variations" but the free boundaries make it a pretty though nut to crack.
$endgroup$
– maxmilgram
Jan 31 at 6:39
$begingroup$
@maxmilgram If the bag is being filled with air, will it still matter how it is supported?
$endgroup$
– Aniruddh Venkatesan
Jan 31 at 21:38