
ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary 
Approximate pi by estimating the ratio of darts, thrown randomly at a dart board, that land inside the circle, to those that land outside.In order to run this problem, Windows users will need to edit the "EscotRunner.lax" file in a text editor. Add this line to the end of the file:
lax.nl.java.option.java.heap.size.max=32000000
If you are using the Escot Runner, you may use the link below to download and try this problem.
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There was only one student response to this problem, so we don't know much about how well students were able to make the connection between the simulation and the probabilities.From the one response, it seems that the students were able to make intuitive decisions based on the relative areas of the circle and square but either did not have the tools to make an explicit comparison, or did not feel that they needed to compute the exact ratio of the areas given the information from the simulations. After several attempts, the students still found the last question  part D  very difficult.
We ran into some memory difficulties on the PC platform for this activity. The default memory for the JDK1.1.8 Virtual machine is 16mb. We needed about 20 or more mb. This can be fixed by changing the configuration files. Windows users will need to edit the "EscotRunner.lax" file in a text editor by adding this line to the end of the file: lax.nl.java.option.java.heap.size.max=32000000