Re: [math-fun] Twenty-dollar question
Catenaries and parabolae are only distinguishable at large scales: http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I still feel that the picture on back of the $20 looks physically wrong. Does anyone else agree? Maybe it's neither a parabola nor a catenary. Jim On Mon, Mar 18, 2013 at 3:31 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Catenaries and parabolae are only distinguishable at large scales:
http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
It doesn't even look particularly parabolic to me. Anyone want to do a side-by-side plot? Charles Greathouse Analyst/Programmer Case Western Reserve University On Mon, Mar 18, 2013 at 3:31 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Catenaries and parabolae are only distinguishable at large scales:
http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If the arch in St. Louis had been a bit larger -- i.e., such that its span were not negligible compared with the radius of the round Earth -- what would be its ideal shape? At 12:31 PM 3/18/2013, Adam P. Goucher wrote:
Catenaries and parabolae are only distinguishable at large scales:
http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp
Are you talking about the chains holding up the light? There's a vertical chain as well, so the "mathematically correct" shape depends on the relative tensions of the chains. As long as the bill matches reality, catenary vs. parabola is irrelevant. http://0.tqn.com/d/dc/1/0/C/J/whitehouse2.jpg --Michael On Mon, Mar 18, 2013 at 3:43 PM, Henry Baker <hbaker1@pipeline.com> wrote:
If the arch in St. Louis had been a bit larger -- i.e., such that its span were not negligible compared with the radius of the round Earth -- what would be its ideal shape?
At 12:31 PM 3/18/2013, Adam P. Goucher wrote:
Catenaries and parabolae are only distinguishable at large scales:
http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
On 3/18/2013 12:43 PM, Henry Baker wrote:
If the arch in St. Louis had been a bit larger -- i.e., such that its span were not negligible compared with the radius of the round Earth -- what would be its ideal shape?
A segment of an ellipse with one foci at the center of the Earth. Brent Meeker
At 12:31 PM 3/18/2013, Adam P. Goucher wrote:
Catenaries and parabolae are only distinguishable at large scales:
http://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg
----- Original Message ----- From: James Propp Sent: 03/18/13 07:03 PM To: math-fun Subject: [math-fun] Twenty-dollar question
Is the hanging chain on the back of the $20 bill mathematically correct? It looks more like a parabola than a catenary to me.
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Interesting! Is there a particular insight that makes this obvious; e.g., would an ellipse-shaped object which didn't intersect the Earth's surface hold its shape? A very large object intersecting the Earth's surface could obviously not be in orbit, as it would be fixed to the Earth. At 04:46 PM 3/18/2013, meekerdb wrote:
On 3/18/2013 12:43 PM, Henry Baker wrote:
If the arch in St. Louis had been a bit larger -- i.e., such that its span were not negligible compared with the radius of the round Earth -- what would be its ideal shape?
A segment of an ellipse with one foci at the center of the Earth.
Brent Meeker
participants (6)
-
Adam P. Goucher -
Charles Greathouse -
Henry Baker -
James Propp -
meekerdb -
Michael Kleber