HISTORY OF PI AND BUFFON’S NEEDLE

This project involves some reading, learning and interactive experimenting with the mathematical value of pi.  This very special mathematical constant has a long and illustrious history and is still being studied and investigated today.  
 
The purpose of this project is to allow you to gain some familiarity with the history and background of the value of pi.  To do so, you will need to visit the MacTutor History of Mathematics Archive site where you will find some excellent materials to facilitate your learning.

You will also make use of an interactive applet for Buffon’s Needle experiment to estimate the value of pi.

Assignment:
 
Part 1:
Visit http://www-history.mcs.st-and.ac.uk/history/HistTopics/Pi_through_the_ages.html and read the article entitled History of Pi.  As you read, please answer the following questions:
 
1.	What approach did Archimedes take in finding an approximation for the value of pi?
2.	What arithmetic formula for pi is sometimes attributed to Leibniz and what was so surprising about it?
3.	What was Gregory’s more general formula for pi involving the arctangent function (arctan x or tanx)?
4.	Who first used the notation π for pi?
 
Part 2:
Access the Java applet for Buffon’s Needle experiment located at http://www.mste.uiuc.edu/reese/buffon/buffon.html.  Click on the link entitled Introduction to the problem and read the information presented there.

Afterwards, click on the link entitled Run the simulation using a Java applet.  Run the applet several times for each of the different numbers of needle drops (viz., 1, 10, 100 and 1000) and observe each of the results in comparison to the true value of pi.  After each set of drops involving a given number of needles, click on the button labeled Start Over in order to clear the applet’s memory.

Lastly, use the applet to answer the following question:

5.	Use Buffon’s Needle applet to estimate the value of pi as accurately as possible.  Explain exactly how you used the applet and your reasoning concerning the best possible accuracy.