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Pi Machine 1
posted April 6, 2000 as
a Math
Forum EPoW
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Introduction: In this part
of the Pi Machine problem series,
students approximate pi by estimating
the ratio of darts, thrown randomly
at a dart board, that land inside
the circle to those that land outside.
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Where's the Math: In
this investigation, students make
predictions and investigate ratios
in geometry by using computer simulations.
Standards: Geometry,
measurement,
number
& operations
Role of Components: The
Pi Machine problem series uses AgentSheets
to generate random points inside
the circles. Swing
slider allows students to change
the radius, simple table
displays data, and number
entry allows students to select
the total number of points in the
simulation. Instructions are displayed
and solutions are entered in a
text entry box. Components are
coordinated with Javascript.
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Try the applet!
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Sample submitted solutions:
(No submitted solutions
received credit for this problem.)
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Reflections:
There was only one student response to this
problem so we don't know much about how
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
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