Application

Application Geometry Technology

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.

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?

Application Geometry

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

By patrick honner, 14 years11 years ago

Application Appreciation

On Flyswatters

Designing a flyswatter is an interesting exercise in optimization.

You want it have enough holes so that it can quickly achieve swatting speed, but you don’t want it to have so many holes as to substantially decrease the chance of actually making contact with the pest.

I wonder if there is an industry standard for a flyswatter’s empty-space-to-surface-area ratio.

By patrick honner, 14 years11 years ago

Application Economics

Movie Pricing

I wonder if there are any theaters that take movie length into account when pricing admission. Last night, I saw “The Girl with the Dragon Tattoo”, which came in around 2.5 hours. Compare that with “Toy Story 3”, which (according to secondary sources) runs approximately 1.6 hours. Basically, for every two showings of TGwtDT, a theater could instead put on three showings of TS3.

I’m sure there are demand issues involved here, but simple logic to me suggests that more showings means more people in the seats, which yields more revenue through admissions and concessions (I’m assuming the margninal cost of showing a movie is negligible). Inversely, a longer movie means fewer viewings and consequently less revenue.

So maybe longer movies should be more expensive? Or shorter movies should be cheaper? As an aside, If quality were a determining factor in price, then I paid too much last night.

By patrick honner, 14 years11 years ago

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