approximation of pi using kedama
Cool. I had a similar one: http://squeakland.org/showcase/project.jsp?id=8937
I like both projects in that they show the how you can use the Monte Carlo method to estimate the area of a circle. But how do you get them to think about and discover for themselves that there is a constant ratio of the area of the circle to the radius^2?
I like Yoshiki's analogy of throwing seeds on a square field, pehaps have the kids try this (only with something of a known area (ie: a square with 1/4 or 1/2 being the target. Then let them figure out how to do this in Etoys. Which could be done without Kedama (as learning Etoys scripting is easier than figuring out how Kedama works, hope to address this at some point through screencasts) although this might be a great introduction as it does not yet introduce Patches).
The Monto Carlo method is a much simpler way for kids to find the area than the one I had originally thought of in my Etoys Challenge: "How to get kids to derive Pi for themselves". And I am debating (and need to test) whether I should use it at the before or after the Archimedes method. I am leaning towards letting them figure out the circumference (as opposed to the area of the regular polygons in that it is easier to make the connection to the ratio to the diameter then the ration to r^2. I could then show r^2 works as well after that. Comments/suggestions welcome.
Okay so the area of the square is the radius squared * 4 (sorry it's late and I'm a little slow) so get them first to think of the ratio of the area of the circle to the square it inscribes. Excellent, thank you!!!
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