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

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----- 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

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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