Buffon’s Needle

Posted: March 6, 2016 in Area, Calculus: An Introduction
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With “Pi day” fast approaching, the timing of this is appropriate. One activity on day one with my introductory calculus students has them throwing toothpicks onto a large sheet of paper containing several strategically spaced parallel lines. After an adequate number of trials, students double that quantity, then divide that result by the number of toothpicks that touched or crossed any line. Once it is determined that the results are always relatively close to π, they want to know why.

This, along with some other discussions and demonstrations, set the stage very nicely for our little journey through introductory calculus. The entry here shows how part of the curiosity initiated on day one will be satisfied.

 

Buffons’ Needle (setup)

Buffon's Needle

 

Function Reflects the Moving Needle

Buffon's Needle2

 

Conclusion

Buffon's Needle4

 

I’ve included additional notes below to set up the interactive link that follows.

No Hit (wrong combination)

Buffon's Needle3Optional1

 

Point of Rotation on Line (always intersecting)

Buffon's Needle3Optional

Click on the link provided here to interact with Buffon’s Needle.

 

Thanks for reading.

 

Reference: http://mste.illinois.edu/activity/buffon/

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