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​ :

π ≈

2 p

≈