Geometry of BBQ

There seemed to be a lot of geometry involved in my grilling this weekend.  The circular grill, the cylindrical chimney starter, the pyramid of coals.  The charcoal briquettes themselves look like solids with mirrored parabolas as vertical cross-sections and squares as horizontal cross-sections.

As I cooked a few times over different coal arrangements, I wondered about the heat distribution on the grill over the perfect pyramid of charcoal.  Obviously the hottest point is the center (nearest the peak of the pyramid), and the temperature drops as you move toward the edge along a radius.  Does it drop linearly?  Like a parabola?  Like a log function?

My guess is it looks like the image below.  I don’t have any evidence for this speculation, but this is a representation of a Gaussian distribution, and when in doubt, go with Gauss.  Gauss seems to have a hand in everything.  Maybe I’ll bring the meat thermometer next time and take some readings.

Water Ellipses?

A funny thing happened on the way to the graphing utility.

I thought I’d use Geogebra to estimate the equation of the water parabola I saw at the Detroit Airport.

So I pasted the photo into Geogebra, dropped five points on the arc, and then used “Construct Conic Through Five Points”.  The results are on the right.

Now the weird part:  the equation is not a parabola, but an ellipse.  I thought that perhaps I had done a poor job of selecting points, but no matter how I chose the points, the equation came up as an ellipse.

Note the presence of both an x² and a y² in the equation below.

Ellipse.Equation

Is this a limitation of Geogebra?  Is this an anomaly caused by rendering the digital picture?  Or is the assumption that the path of the water is parabolic faulty?

Related Posts

 

Water Parabolas

It’s not easy to see, but at the right is a picture of the famous water parabolas at the Detroit Airport.  The parabola certainly is a favorite among the fountain designer.  I wonder why?

Upon closer inspection, I’m not sure it’s a parabola!  Check out my attempt to find the equation of this parabola using Geogebra.

And here is a lovely video of the water feature in action:  http://www.youtube.com/watch?v=VSUKNxVXE4E

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