Re: [math-fun] Spirography
Date: Mon, 16 Jun 2014 11:54:40 -0400 [in issue 29] From: James Propp <jamespropp@gmail.com>
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? The knockoff product I have, has holes in both parts, suitable for pushing pins through, so in theory you only have to push on the pen tip. Rather than a wax tray the first thing I'd think of would be corrugated cardboard & the second, cork. I'm imagining something like a latchable/unlatchable zipper. That's a fascinating idea in itself. It could be used in funicular railways, for instance.
Although the zipper tooth design is asymmetrical, I have a coat that unzips from both ends. --Steve
Gosper, is Julian all pessimistic because the classic spirograph has the rotor rolling around the inside of the stator? Does the problem persist if the rotor rolls around the outside? On Wed, Jun 18, 2014 at 4:23 PM, Steve Witham <sw@tiac.net> wrote:
Date: Mon, 16 Jun 2014 11:54:40 -0400 [in issue 29]
From: James Propp <jamespropp@gmail.com>
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force?
The knockoff product I have, has holes in both parts, suitable for pushing pins through, so in theory you only have to push on the pen tip. Rather than a wax tray the first thing I'd think of would be corrugated cardboard & the second, cork.
I'm imagining something like a latchable/unlatchable zipper.
That's a fascinating idea in itself. It could be used in funicular railways, for instance.
Although the zipper tooth design is asymmetrical, I have a coat that unzips from both ends.
--Steve
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Don't recall seeing this mentioned on math-fun: In Jan., there was an article in the NY Times about how when a chain stuffed into a container open at the top, and one end is tossed over the side with lots of room to fall (e.g., letting it drop over a balcony), the chain falls into a pattern with the chain initially rising surprisingly high before it falls -- looking like a fountain. If you don't want to hear the explanation right away so you can think about it, stop this video soon after 1:00. (The explanation begins soon after 1:15.) http://www.nytimes.com/video/science/100000002747620/fountains-of-chain.html... (1 minute 47 seconds).* Even with the explanation, I still find this amazing. --Dan __________________________________________ * Unfortunately, to watch the video you apparently must watch the ad before it, but I didn't find this too painful.
Even with the explanation, I still find this amazing.
This is indeed wonderful. I wonder if it accounts for cases of chains hopping off of pulleys. It seems that if the explanation is correct, the phenomenon shold depend on the compressibility of the chain; suppose it had long thing links? Or rubber links? Whit
The explanation suggested in the video struck me as unconvincing. Leverage might well explain the S-curve at the top of the fountain, yes. However the rising segment could apparently result from the upward acceleration applied to a link by the (virtual) pulley over the edge of the vessel. Now an intriguing stability question arises --- what determines the height of this pulley? Well, it might be the elasticity of the links, or it might be the height of the drop. I'd want to compare of different elastic coefficients and drop heights. Fred Lunnon On 6/19/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
Even with the explanation, I still find this amazing.
This is indeed wonderful. I wonder if it accounts for cases of chains hopping off of pulleys. It seems that if the explanation is correct, the phenomenon shold depend on the compressibility of the chain; suppose it had long thing links? Or rubber links?
Whit
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I'd be surprised if the height of the drop was significant, provided it's at least a few times the height of the fountain. (Less than that and it might damp the action somewhat by the same rebound mechanism.) Charles Greathouse Analyst/Programmer Case Western Reserve University On Thu, Jun 19, 2014 at 9:17 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The explanation suggested in the video struck me as unconvincing. Leverage might well explain the S-curve at the top of the fountain, yes. However the rising segment could apparently result from the upward acceleration applied to a link by the (virtual) pulley over the edge of the vessel.
Now an intriguing stability question arises --- what determines the height of this pulley? Well, it might be the elasticity of the links, or it might be the height of the drop. I'd want to compare of different elastic coefficients and drop heights.
Fred Lunnon
On 6/19/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
Even with the explanation, I still find this amazing.
This is indeed wonderful. I wonder if it accounts for cases of chains hopping off of pulleys. It seems that if the explanation is correct, the phenomenon shold depend on the compressibility of the chain; suppose it had long thing links? Or rubber links?
Whit
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The paper is on the arXiv: http://arxiv.org/pdf/1310.4056.pdf On Thu, Jun 19, 2014 at 9:47 AM, Charles Greathouse < charles.greathouse@case.edu> wrote:
I'd be surprised if the height of the drop was significant, provided it's at least a few times the height of the fountain. (Less than that and it might damp the action somewhat by the same rebound mechanism.)
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Thu, Jun 19, 2014 at 9:17 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The explanation suggested in the video struck me as unconvincing. Leverage might well explain the S-curve at the top of the fountain, yes. However the rising segment could apparently result from the upward acceleration applied to a link by the (virtual) pulley over the edge of the vessel.
Now an intriguing stability question arises --- what determines the height of this pulley? Well, it might be the elasticity of the links, or it might be the height of the drop. I'd want to compare of different elastic coefficients and drop heights.
Fred Lunnon
On 6/19/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
Even with the explanation, I still find this amazing.
This is indeed wonderful. I wonder if it accounts for cases of chains hopping off of pulleys. It seems that if the explanation is correct, the phenomenon shold depend on the compressibility of the chain; suppose it had long thing links? Or rubber links?
Whit
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-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
That's a nice paper: readable, informative, well researched. I'm convinced. WFL On 6/19/14, Neil Sloane <njasloane@gmail.com> wrote:
The paper is on the arXiv: http://arxiv.org/pdf/1310.4056.pdf
On Thu, Jun 19, 2014 at 9:47 AM, Charles Greathouse < charles.greathouse@case.edu> wrote:
I'd be surprised if the height of the drop was significant, provided it's at least a few times the height of the fountain. (Less than that and it might damp the action somewhat by the same rebound mechanism.)
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Thu, Jun 19, 2014 at 9:17 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The explanation suggested in the video struck me as unconvincing. Leverage might well explain the S-curve at the top of the fountain, yes. However the rising segment could apparently result from the upward acceleration applied to a link by the (virtual) pulley over the edge of the vessel.
Now an intriguing stability question arises --- what determines the height of this pulley? Well, it might be the elasticity of the links, or it might be the height of the drop. I'd want to compare of different elastic coefficients and drop heights.
Fred Lunnon
On 6/19/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
Even with the explanation, I still find this amazing.
This is indeed wonderful. I wonder if it accounts for cases of chains hopping off of pulleys. It seems that if the explanation is correct, the phenomenon shold depend on the compressibility of the chain; suppose it had long thing links? Or rubber links?
Whit
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-- Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (7)
-
Allan Wechsler -
Charles Greathouse -
Dan Asimov -
Fred Lunnon -
Neil Sloane -
Steve Witham -
Whitfield Diffie