Unraveling a ball of yarn from the inside
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
favorite
My experience is that if you can smoothly unravel a ball of yarn from the outside, you can also smoothly unravel it from the inside---if you can get hold of the end buried in the ball and cope with the ball going floppy once the core has been removed.
Is this mathematically or thought-experimentally provable?
UPDATE (MORE DETAIL): I am interested in the behavior of real world balls of yarn (e.g. sheep wool). Specifically, I want to know whether a certain way of wrapping a ball of yarn might introduce some kind of knot or tangle that prevents it from being unwound from the inside-out, yet still allows it to be unwound from the outside-in.
general-topology
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
add a comment |Â
up vote
3
down vote
favorite
My experience is that if you can smoothly unravel a ball of yarn from the outside, you can also smoothly unravel it from the inside---if you can get hold of the end buried in the ball and cope with the ball going floppy once the core has been removed.
Is this mathematically or thought-experimentally provable?
UPDATE (MORE DETAIL): I am interested in the behavior of real world balls of yarn (e.g. sheep wool). Specifically, I want to know whether a certain way of wrapping a ball of yarn might introduce some kind of knot or tangle that prevents it from being unwound from the inside-out, yet still allows it to be unwound from the outside-in.
general-topology
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
My experience is that if you can smoothly unravel a ball of yarn from the outside, you can also smoothly unravel it from the inside---if you can get hold of the end buried in the ball and cope with the ball going floppy once the core has been removed.
Is this mathematically or thought-experimentally provable?
UPDATE (MORE DETAIL): I am interested in the behavior of real world balls of yarn (e.g. sheep wool). Specifically, I want to know whether a certain way of wrapping a ball of yarn might introduce some kind of knot or tangle that prevents it from being unwound from the inside-out, yet still allows it to be unwound from the outside-in.
general-topology
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
My experience is that if you can smoothly unravel a ball of yarn from the outside, you can also smoothly unravel it from the inside---if you can get hold of the end buried in the ball and cope with the ball going floppy once the core has been removed.
Is this mathematically or thought-experimentally provable?
UPDATE (MORE DETAIL): I am interested in the behavior of real world balls of yarn (e.g. sheep wool). Specifically, I want to know whether a certain way of wrapping a ball of yarn might introduce some kind of knot or tangle that prevents it from being unwound from the inside-out, yet still allows it to be unwound from the outside-in.
general-topology
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
edited Aug 21 at 9:53
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
asked Aug 21 at 8:46
ᴇʟᴇvᴀтᴇ
1263
1263
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.
answered Aug 21 at 9:05
badjohn
3,4551618
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.
answered Aug 21 at 9:05
badjohn
3,4551618
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
add a comment |Â
up vote
0
down vote
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.
answered Aug 21 at 9:05
badjohn
3,4551618
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
add a comment |Â
up vote
0
down vote
up vote
0
down vote
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.
answered Aug 21 at 9:05
badjohn
3,4551618
It depends a bit on what you are allowed to do. If I am allowed a very long, thin, flexible pair of tweezers that can be directed inside the ball then I start at the external end, trace along the thread to the other end, and then pull it back along itself.
However, if the tweezers are straight then it is rather less obvious. If the tweezers are only as long as the radius rather than the diameter it is harder again, as unless the inner end is in the centre, the choice of entry points is limited.
Friction is also relevant. If the thread is slippery enough then the whole thread may just slide along and you will see the out end move as you start to pull the inner end.
answered Aug 21 at 9:05
badjohn
3,4551618
answered Aug 21 at 9:05
badjohn
3,4551618
answered Aug 21 at 9:05
badjohn
3,4551618
answered Aug 21 at 9:05
badjohn
3,4551618
3,4551618
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
add a comment |Â
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
I love the idea of a ball of frictionless yarn. How would it even stay as a ball?! The question was actually meant to be about real world yarns, like a ball of wool. E.g. if you leave a length of the wool sticking out and then wrap the rest of the wool around and around it self, you have access to both ends of the ball and can unravel it from the outside or the inside, without even needing tweezers.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:18
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Well, I said "slippery enough" rather completely frictionless. The more real your model gets, the harder it will be to answer. If the friction is too high then it might be impossible despite what the maths says. Add a bit more detail to your question on what is and is not allowed. I will think some more and others might contribute.
– badjohn
Aug 21 at 9:34
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
Thanks badjohn, I've added more detail.
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 9:55
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
There is a whole subject of knot theory but we may need some more information. Is the ball created in a typical fashion by just winding the thread around the existing ball? Or can you interleave the thread? Look up the Gordian Knot, could that occur?
– badjohn
Aug 21 at 15:20
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
My thesis is that if you can unwind it from the outside, you can also unwind it from the inside. I'm not disallowing interleaving, so long as it's still possible to unwind it smoothly (i.e. without having to do any special moves to undo knots) from the outside. Is it possible to create a Gordian Knot that falls apart when you pull from the outside but locks in place when you pull from the inside?
– á´‡ÊŸá´‡vᴀтᴇ
Aug 21 at 15:51
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2889628%2funraveling-a-ball-of-yarn-from-the-inside%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
