Comments on: Parabola v. Catenary

By: Caleb

Caleb — Mon, 24 Oct 2011 19:27:31 +0000

I happened across this blog while looking for pictures of falling painos (linked from http://radar.oreilly.com/2009/06/when-do-your-beliefs-become-kn.html). And I started reading Dan’s blurg on infographics. Then I saw Dan spin off this thread on can-thingys and parab-thingys (on purpose using ‘thingy’).
I rarely comment, if ever, on blogs but I have to say just 3 things:
1) My context – loved math my whole life, minored in it in college, wouldn’t now be able to reproduce even half of whatever it was a learned back then

2) I found both the PR thread and this thread facinating!

3) I still don’t really understand what you guys are taking about: Catenary vs. Parabola other than there is some difference mathematically that may or may not be relevant to you depending on if you’re a match major, architect, song writter, or poet. So if I find the topic interesting enough to read the whole thing ,but still complex enough not to really understand it – how is a 12 year old supposed to understand the discussion?

Anyway, thanks for an enjoyable 30 minute lunch break!

PS really far away from the thread…most useful math concept in my life: A AND B = NOT A OR NOT B

By: Chris Sears

Chris Sears — Sat, 22 Oct 2011 05:04:56 +0000

Here are the photos I worked on for McDonald's.

By: Den Rattee

Den Rattee — Sat, 22 Oct 2011 03:58:16 +0000

@Tony — Ha! Love it – it’s all but proved.

By: Tony

Tony — Sat, 22 Oct 2011 03:23:48 +0000

I inserted the picture into my TI-Nspire Software, plotted about 7 points and then performed a quadratic regression. My R^2 value was 99% and it looked pretty darn good…much better than the catenaries I’ve used in similar investigations with my class. Based on my previous studies into catenaries vs. parabolas I thought for sure this was a parabola but all this discussion has me confused. Hey…the calculator says it’s right so then it must be…

By: Chris Sears

Chris Sears — Sat, 22 Oct 2011 02:37:52 +0000

Eric B.:
I would think the most famous parabola in America would be the “double parabola” of McDonald’s.

Mark:
I like the idea of putting the picture on graph paper, but I think it would be nice in a more advanced class to pick three points, solve the resulting system of equations and get an equation for a parabola.

Well, it just so happened that I was at McDonald’s tonight for a mass play date with my children’s friends, and I am teaching quadratic modeling in my College Algebra class. So, inspired by Eric, I grabbed a place mat, scanned the Golden Arches ® into the computer, and dumped the picture into GeoGebra.

It turns out that the Golden Arches ® is not a parabola at all. It turns out that they are best described by ellipses. I’m working out a few pictures now.

By: Why do I keep teaching projectile motion? « Physics and Barbells

Why do I keep teaching projectile motion? « Physics and Barbells — Fri, 21 Oct 2011 16:48:07 +0000

[…] the one hand, parabolas are all over the place. Not always where we’re told we see them, but still, they’re around. For low speed heavy things they work pretty darn well. The last […]

By: Mark

Mark — Fri, 21 Oct 2011 14:46:53 +0000

I like the idea of putting the picture on graph paper, but I think it would be nice in a more advanced class to pick three points, solve the resulting system of equations and get an equation for a parabola. I think this bridge is a catenary, so the initial equation might look quite close, but not exactly the same. If the students had already done the same activity with a suspension bridge that actually formed a parabola, you could talk about why this wasn’t an exact fit. If the class had discussed hyperbolic cosine functions previously then you could lead them in that direction. For a more elementary class, you could have students compete to find the best fit with a parabola by changing the parameters. At the end, you reward the students that got the closest, and if you want to talk about physics tell them what the catenary is.

By: Brendan Murphy

Brendan Murphy — Fri, 21 Oct 2011 02:54:46 +0000

Thanks for the quote Vishakha, I think I will use it in my email signature.

As to the parabola or catenary, flattened or otherwise. I think it is well suited for 8th grade high school algebra. We can take this picture put it on a graph and discover that it isn’t actually a parabola.

By: Mr Macx

Mr Macx — Thu, 20 Oct 2011 17:56:20 +0000

So, I know these are different curves, but can’t we curve fit a parabola onto this arch within the finite space of the poster? The curves behave in different ways, but that is at larger limits than what i’m looking at. At least, that’s always been my impression. In a relatively small finite amount of space, I can create a catenary or a parabola that look identical to the naked eye.

By: Mark

Mark — Wed, 19 Oct 2011 23:50:04 +0000

Thanks David. I see what you mean now. That makes complete sense and I agree with you about that being a big deal. Sorry to get so off topic Dan.