HISTORY OF PI AND BUFFON’S NEEDLE		Write-pair-share

Visit Buffon’s Needle applet, http://www.math.csusb.edu/faculty/stanton/probstat/buffon.html This applet allows the user to view the cumulative effects of dropping needles in a probability experiment involving the value of pi.

Part 1
Record the successive values produced by Buffon’s Needle applet when dropping the number of needles indicated in the table below in successive increments of 20.

To do so, first select 20 needles in the dropdown menu for number of needles (you may have to click twice on the dropdown menu before it appears); then, click repeatedly on the button labeled play and record the approximate value for pi after each click.  The successive values in the textbox labeled 2/X are the successive approximations for the value of pi.

number of 
needles dropped	approx value of pi
(2/X)		number of 
needles dropped	approx value of pi
(2/X)	
20 			200		
40			220		
60			240		
80			260		
100			280		
120			300		
140			320		
160			340		
180			360		

Part 2
Based on your recorded data, discuss the following questions with your partner and record your answers:

1.	Does the approximate value for pi become increasingly more accurate with each successive 20 needles dropped? 

2.	Does the approximate value for pi become increasingly more accurate with each successive 100 needles dropped?

3.	How close to the real value of pi would you expect the approximate value to be after 1000 needles were dropped?  

4.	Is there an optimal number of needles dropped that produces the best approximation of pi?  If so, what is that number?