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Tuesday, April 7, 2009

Real World Once Again Inconvenient

Here are three attempts to model "Will the Ball Hit the Can?" in Sketchpad:

Attempt 1: I try to make the grid scale match the given scale. (1 unit = 1 yard? Or close to it?) This requires the coefficient of the squared to term to be waaaay to small for clumsy freshman fingers.

Attempt #2: Make the scale very large. Now the leading coefficient is a little more friendly, but by comparison I have to make the constant coefficient slider way too short.

Attempt #3: Using a rectangular grid, so that the y axis is a relatively smaller scale than the x axis. Now all three coefficients are lengths I think the freshmen can handle. The catch? We can't even pretend this function means anything any more.
I'm going with #3, but it will bother me; I feel like I am perpetrating a ruse. On the other hand, I have learned way more about the behavior of the standard form of a parabola than I would have had I not bothered to try.
Feel free to email me if you want the sketchpad file to play with. It's 32MB.