Name ____________________________ Date ____________ Assignment # ______
Buffon’s Needle Experiment to Approximate Pi In mathematics , Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon : Suppose we have a floor made of parallel strips of wood , each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?
We are going to use toothpicks to recreate this experiment and maybe we will get a nice “Pi” surprise when we are finished! ● Draw parallel lines on a sheet of paper. Make sure that the distance between each parallel line is exactly the length of the toothpick. ● Make sure your sheet of paper is on a flat surface such as a table top or the floor. ● Drop the toothpick onto the paper and record whether it lands:
A: Not touching a line B: Touching or crossing a line Now drop the toothpick 100 times and record below. toothpick lands
Tally
Frequency
Percentage
Totals:
100
100%
A (no touch)
B (crosses)
Now let’s estimate pi! Buffon used the results from his experiment with a needle to estimate the value of π . He worked out this formula:
π ≈
2L xp
where L = length of needle (toothpick) x = parallel line spacing p = percent of needles (toothpicks) crossing a line (Case B) - express as decimal
In our case L = x, so our simplified Pi approximation formula is:
π ≈
2 p
● So, what is YOUR GROUP ESTIMATION of pi after your 100 trials?
π ≈
2 p
≈
Share your data with the teacher so we can have a classroom estimation of pi using this experiment. ● Class Approximation :
Page 1 of 2. Name. Date ______ Assignment # ______. Buf on. 's Needle Experiment to Approximate Pi. In mathematics, Buffon's needle problem is a question. first posed in the 18th century by Georges-Louis Leclerc,. Comte de Buffon: Suppose we have a floor made of. parallel strips of wood, each the. same width, and ...
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