[math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments. Jim Propp
I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments. I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome. Jim Propp On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
Jim Propp
Hi Jim, You asked about the hypocycloid with gears in ratio 2:1 being used in a straight-line mechanism. That possibility was well known in the 1800s but I don't know examples of its practical use. See for example Mechanism 329 in the book 507 Mechanical Movements: http://507movements.com/mm_329.html In your discussion of MoMath, I think you miss a bigger point that part of the intention in the exhibits is to show people that Math is Cool (I even put that literally on the walls of the rest rooms) and is a living, creative subject. When explaining the square wheeled trike exhibit, besides the issue of catenaries, I also try to explain that the more math you know the more cool things you can think of and create, and that math is valuable for creative arts and design in addition to the usual subjects people think of when talking about applied mathematics. These aspects of mathematics that are obvious to mathematicians are not well understood by the public. George http://georgehart.com On 7/1/2015 10:59 PM, James Propp wrote:
I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments.
I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome.
Jim Propp
On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
When an author describes something as "cool", unless it has to do with temperature, I tend to think the author is an idiot, and I move on to something else. -- Gene From: George Hart <george@georgehart.com> To: math-fun@mailman.xmission.com Sent: Thursday, July 2, 2015 6:36 AM Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike" Hi Jim, You asked about the hypocycloid with gears in ratio 2:1 being used in a straight-line mechanism. That possibility was well known in the 1800s but I don't know examples of its practical use. See for example Mechanism 329 in the book 507 Mechanical Movements: http://507movements.com/mm_329.html In your discussion of MoMath, I think you miss a bigger point that part of the intention in the exhibits is to show people that Math is Cool (I even put that literally on the walls of the rest rooms) and is a living, creative subject. When explaining the square wheeled trike exhibit, besides the issue of catenaries, I also try to explain that the more math you know the more cool things you can think of and create, and that math is valuable for creative arts and design in addition to the usual subjects people think of when talking about applied mathematics. These aspects of mathematics that are obvious to mathematicians are not well understood by the public. George http://georgehart.com
How sad---you're probably missing lots of cool stuff! On Thu, Jul 2, 2015 at 9:12 AM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
When an author describes something as "cool", unless it has to do with temperature, I tend to think the author is an idiot, and I move on to something else.
-- Gene
From: George Hart <george@georgehart.com> To: math-fun@mailman.xmission.com Sent: Thursday, July 2, 2015 6:36 AM Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
Hi Jim,
You asked about the hypocycloid with gears in ratio 2:1 being used in a straight-line mechanism. That possibility was well known in the 1800s but I don't know examples of its practical use. See for example Mechanism 329 in the book 507 Mechanical Movements: http://507movements.com/mm_329.html
In your discussion of MoMath, I think you miss a bigger point that part of the intention in the exhibits is to show people that Math is Cool (I even put that literally on the walls of the rest rooms) and is a living, creative subject. When explaining the square wheeled trike exhibit, besides the issue of catenaries, I also try to explain that the more math you know the more cool things you can think of and create, and that math is valuable for creative arts and design in addition to the usual subjects people think of when talking about applied mathematics. These aspects of mathematics that are obvious to mathematicians are not well understood by the public.
George http://georgehart.com
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
While I would not have expressed it quite so baldly, I do think Gene makes a valid point here --- admittedly concerning George's style rather than Jim's. The trouble with briefly fashionable jargon such as "cool" (along with heaven knows how many similarly irritating terms of approbation) is that it pigeonholes its author within some recent but no longer fashionable generation, thereby both losing respect from any later waves with which he may have been intending to ingratiate himself, as well as appearing juvenile to those more (unapologetically) antique. Fred Lunnon On 7/2/15, Mike Stay <metaweta@gmail.com> wrote:
How sad---you're probably missing lots of cool stuff!
On Thu, Jul 2, 2015 at 9:12 AM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
When an author describes something as "cool", unless it has to do with temperature, I tend to think the author is an idiot, and I move on to something else.
-- Gene
From: George Hart <george@georgehart.com> To: math-fun@mailman.xmission.com Sent: Thursday, July 2, 2015 6:36 AM Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
Hi Jim,
You asked about the hypocycloid with gears in ratio 2:1 being used in a straight-line mechanism. That possibility was well known in the 1800s but I don't know examples of its practical use. See for example Mechanism 329 in the book 507 Mechanical Movements: http://507movements.com/mm_329.html
In your discussion of MoMath, I think you miss a bigger point that part of the intention in the exhibits is to show people that Math is Cool (I even put that literally on the walls of the rest rooms) and is a living, creative subject. When explaining the square wheeled trike exhibit, besides the issue of catenaries, I also try to explain that the more math you know the more cool things you can think of and create, and that math is valuable for creative arts and design in addition to the usual subjects people think of when talking about applied mathematics. These aspects of mathematics that are obvious to mathematicians are not well understood by the public.
George http://georgehart.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
A cool thing is that a square rotating on a catenary is is the inverse of a parabola rotating on a line. The interesting questions are "why is a hanging chain the roulette of a parabola?" "why does a hanging chain have a succinct expression?" and "what does gravity have to do with it?" Hilarie
Date: Wed, 1 Jul 2015 22:59:09 -0400 From: James Propp <jamespropp@gmail.com> Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments.
I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome.
Jim Propp
On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
Jim Propp
Here's another cool thing George Hart wrote about in a paper that I recently incorporated into a book I'm editing for the MAA. Look at this photo of a rubber band on George's fingers: https://www.flickr.com/photos/thane/18741252973/in/dateposted-public/ Now pick up a rubber band yourself with one hand, and see if you can figure out how get that rubber band into that same "Pentadigitation" configuration onto your own fingers without using your other hand to help you. Just figuring out to get it onto one hand's fingers with *two hands* is already tricky. But George explains how to do it with one hand. Cool. BTW, if "cool" is a dated word, perhaps "fun," as in "math-fun", is also? Maybe my participation in a "fun" forum suggests my possible membership in a no longer fashionable generation, perhaps one even composed of "idiots"? It would be good to know. On Thu, Jul 2, 2015 at 1:10 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
A cool thing is that a square rotating on a catenary is is the inverse of a parabola rotating on a line.
The interesting questions are "why is a hanging chain the roulette of a parabola?" "why does a hanging chain have a succinct expression?" and "what does gravity have to do with it?"
Hilarie
Date: Wed, 1 Jul 2015 22:59:09 -0400 From: James Propp <jamespropp@gmail.com> Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments.
I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome.
Jim Propp
On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Cannon balls seek ellipses rather than parabolas. How does planetary roundness (point source gravity) distort catenaries? --rwg Supposedly, with the weight of the roadway, the Golden Gate Bridge cables changed from catenaries to parabolas. But what, really? The errors might be observable: The tops of the towers are inches further apart than the bottoms. On 2015-07-02 13:10, Hilarie Orman wrote:
A cool thing is that a square rotating on a catenary is is the inverse of a parabola rotating on a line.
The interesting questions are "why is a hanging chain the roulette of a parabola?" "why does a hanging chain have a succinct expression?" and "what does gravity have to do with it?"
Hilarie
Date: Wed, 1 Jul 2015 22:59:09 -0400 From: James Propp <jamespropp@gmail.com> Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike"
I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments.
I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome.
Jim Propp
On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I don't know if this applies, but I think I used to read that at least the Bay Bridge's cables were parabolas not due to the weight of the roadway but because that was structurally the strongest. But I have no details or source. —Dan
On Jul 2, 2015, at 3:02 PM, rwg <rwg@sdf.org> wrote:
Cannon balls seek ellipses rather than parabolas. How does planetary roundness (point source gravity) distort catenaries? --rwg Supposedly, with the weight of the roadway, the Golden Gate Bridge cables changed from catenaries to parabolas. But what, really? The errors might be observable: The tops of the towers are inches further apart than the bottoms.
On 2015-07-02 13:10, Hilarie Orman wrote:
A cool thing is that a square rotating on a catenary is is the inverse of a parabola rotating on a line. The interesting questions are "why is a hanging chain the roulette of a parabola?" "why does a hanging chain have a succinct expression?" and "what does gravity have to do with it?" Hilarie
Date: Wed, 1 Jul 2015 22:59:09 -0400 From: James Propp <jamespropp@gmail.com> Subject: Re: [math-fun] Draft of "The Lessons of a Square-Wheeled Trike" I included the draft as an attachment in my earlier email, forgetting that "we" (math-fun) don't "do" attachments. I've posted the draft at http://mathenchant.org/8-museum.rtf ; comments are welcome. Jim Propp On Tue, Jun 30, 2015 at 3:35 PM, James Propp <jamespropp@gmail.com> wrote:
I've finished a draft of installment #1 (as opposed to #0) of "Mathematical Enchantments", and I'd welcome comments.
participants (9)
-
Dan Asimov -
Eugene Salamin -
Fred Lunnon -
George Hart -
Hilarie Orman -
James Propp -
Mike Stay -
rwg -
Thane Plambeck