Saturday, October 22, 2011

The Golden Arches ® Exposed!

On the blog dy/dan, there was a recent discussion about the shape of a bridge.  One commenter joked about the Golden Arches of McDonald's as being the most famous parabolas in America.  As I am teaching quadratic modeling in College Algebra right now, I though I would find an equation for these parabolas.  The problem is that the Golden Arches are not parabolas.

To find the equation, I scanned the Golden Arches from a placemat that I found at McDonald's tonight.  I took the scanned picture and imported it into GeoGebra.  I picked five points on the outside of one arch, and five points inside of the arch.  The picture is below.
Ten points through the Golden Arch
For the outside of the arch, I chose the points (0,0), (3.73, 11.8), and (6.62, 7.87).  By many calculations, I got the parabola y = -0.68329x^2 + 5.71222x.  After even more calculations to get the focus and directrix, I was able to graph the parabola in GeoGebra.  I used the program Maxima to perform the calculations.  The parabola is below.
The parabola through the points on the outside of the arch
For the inside of the arch, I chose the points (1.63, 0), (3.73, 10.94), and (5.86, 0.86).  The parabola I got was y = -2.35034x^2 + 17.80732x - 22.78133.  The second parabola went much faster because I was able to reuse my Maxima worksheet from the previous parabola.  The graph is below.
The parabola through the points on the inside of the arch.
Just on a lark, I used the conic section tool in GeoGebra to draw the conic sections through the two sets of five points for each arch.  Geogebra came up with two ellipses to pass through the points.  The ellipses look like they match the boundary of the arches pretty well.
Ellipses work well to model the arches

Tuesday, October 18, 2011

I'm Attempting to Summon My Inner Dan Meyer

I got to meet Dan Meyer in person two weekends ago at KCTM.  He is very greatous in person.  He was nice enough to let me take this picture.  You can see how deep the hole is in which I am standing.
Geeking out about iPad cameras.
I've been a believer in what Dan has been promoting for a while.  I developed some of the same notions independently, but Dan has taken it much farther than I would have on my own.

I've been playing around with developing my own materials in the same vein as Dan.  My target audience is different than his, as I mostly teach Intermediate Algebra/Algebra II and higher.  Here's a sample of what I've been working on.  I'm rebooting remaking Dan's basketball video with a slightly different take.  I've got a few sequels planned as well.  My week-old YMCA membership has already payed off.
Built with Adobe Premier Elements and GeoGebra 4
A cleaner version with just the data
(Actually, Dan is leaning down in that picture.)

Tuesday, October 4, 2011

Bye-bye to my iPad

I returned my iPad to the college yesterday.  However, it wasn't a sad day because it was replaced by an iPad 2.
Out with the old, in with the new.
I wasn't too impressed with the first generation iPad.  My biggest complaint is that you cannot duplicate the screen to a projector through the VGA adapter for every app.  There were a few apps that would allow it, but not enough.  The iPad 2 does duplicate the screen, so the whole class can see what I am looking at on my iPad 2.

The new iPad is lighter and thinner than the first generation.  It's not much of a different, but it is still noticeable.  My one concern is that I'll forget that I'm carrying it, put it down, and walk away without it.

I'm still not sure how I'm going to use it in the classroom, but I'm looking forward to figuring out how.  One of the advantages over our SmartBoard is that I can switch between apps quickly.  The disadvantage over the SmartBoard is that I can't record what was shared with the students to post on the class BlackBoard site.  In addition, one of our experiments will be using FaceTime or Skype for virtual office hours.

My old iPad was handed down to one of my colleagues.  According to his Facebook account, he is very happy with it.