Have a Piece of Pi - It is more than a dessert

Introduction

A Brief History of Pi


Ancient civilizations knew that there was a fixed ratio of circumference to diameter that was approximately equal to three. The Greeks refined the process and Archimedes is credited with the first theoretical calculation of Pi.

In 1761 Lambert proved that Pi was irrational, that is, that it can't be written as a ratio of integer numbers.

In 1882 Lindeman proved that Pi was transcendental, that is, that Pi is not the root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time. 

How many digits are there? Does it ever end?

Because Pi is known to be an irrational number it means that the digits never end or repeat in any known way. But calculating the digits of Pi has proven to be an fascination for mathematicians throughout history. Some spent their lives calculating the digits of Pi, but until computers, less than 1,000 digits had been calculated. 

Task

Answer the following questions by following the embedded links (blue/purple underlined words). Please anser the questions on a word document that you will print off and turn it when this WebQuest is complete.

  1. Write the definition of Pi in your own words and a diagram/figure to represnt your definition.
  2. When is Pi Day? Why do you think Pi Day is celebrated?
  3. Review the value of Pi using the Nilakantha series. (Click on the link and glance through the website about finding Pi yourself)
    1. Complete the first two questions from the "your turn." (Show all your steps)
    2. Complete the Activity: Find an Approximate Value For Pi
  4. Use the website, Piece of Pi,  created by your teacher to answer the folowing questions:
    1. Give me two facts about the history of Pi that you didn't know before.
    2. Who could recite 31 digits of Pi when she was 3?
Conclusion

A Cool Pi Experiment


One of the most interesting ways to learn more about Pi is to do pi experiments yourself (Like the activity you did in question 3). Here is a famous one called Buffon's Needle.

In Buffon's Needle experiment you can drop a needle on a lined sheet of paper. If you keep track of how many times the needle lands on a line, it turns out to be directly related to the value of Pi.

Credits

Information for the Introduction and Conclusion came from http://www.math.com/tables/constants/pi.htm.

Other websites based on the links.