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Chain of Pi

The number π is a mathematical constant, represented by the 16th letter of the Greek alphabet "π" since the mid-18th century, and is spelled out as "Pi". It is also referred to as Archimedes' constant.

Pi is the number you get when you divide the circumference of a circle by its diameter.

Pi is an important number used in many different areas of mathematics and geometry. Pi is used in most calculations for building and construction, quantum physics, communications, music theory, medical procedures, air travel, and space flight, to name a few.

Pi is an irrational number, which means that it cannot be expressed by a simple fraction. and that the digits after the decimal go on forever without any regularly repeating segments. As of March 2019, humans have calculated Pi to over 31,400, 000, 000, 000 digits – that’s 31.4 trillion places.

The first few digits of Pi are 3.14, which correspond to March 14th (3/14), so we celebrate the number Pi on this day. If you were to celebrate Pi day with actual pie, you can serve it on March 14 at 3:09pm + 26 seconds. Get it? 03/14 15:09:26

This activity translates the numbers that make up Pi into a colour code. By turning this into a visual it might be easier to understand that there is no pattern to Pi!

Objectives

  • Learn about Pi

    • Learn about irrational numbers
    • Create a visual representation of Pi

Materials

  • Per Project:

    • 10 different colors of colored paper (1 color to represent 1 of each of the 10 digits 0-9)
    • Scissors/paper cutter
    • Stapler and a box of extra staples (or rolls of scotch tape)
    • Printout with the first 500 digits of Pi = “Pi Page
    • A pencil or pen

Key Questions

  • What is Pi? How is it represented? How is it calculated?
  • Who might calculate with Pi? Why?
  • How is Pi used in everyday life?
  • When might one need to calculate a circle's diameter? Why?
  • When might one need to calculate the are of a circle? Why?

What To Do

Preparations

  1. Pre-cut colored paper into long rectangles (a letter sized page can be cut into 4 long strips: 4 cm (2 1/8”) wide by 27.94 cm (11 inches) long)
  2. Assign each color a digit from 0 – 9 (for example: blue = 0, red = 1, yellow =2, etc)
  3. Arrange piles of rectangles by color/digit on a table next to the Pi Page (and a pen/pencil), and a stapler.

Instructions

  1. Find the first digit of Pi (3) on the Pi Page.
  2. Take the corresponding colored rectangle and staple the ends together to make a ring.
  3. Cross out the first digit of Pi on the Pi Page.
  4. Find the second digit of Pi (1).
  5. Take the corresponding colored rectangle and put it through the first ring.
  6. Staple the ends of the rectangle together to make a second ring linked to the first ring (like a chain).
  7. Cross out the second digit on the Pi Page.
  8. Repeat the process, linking a new ring to the previous ring.

Teacher Tip:  If you lose your place in the list of digits at any point, or if you realize that the wrong colour was added, don’t worry! It’s just for fun; the occasional mistake is not a problem.

Extensions

  • Can you make a Pi chain long enough to go around your classroom? How many digits long is it?
  • Can you estimate how long a chain with 1,000 digits of pi would be? 10,000 digits?  1 million digits?
  • What features of natural objects can be quantified by using Pi? On earth? In outer space?
  • Calculate the circumference of one of the rings of paper!

Other Resources

Better Explained | Prehistoric Calculus: Discovering Pi

Math Centre | How did Archimedes Calculate Pi?

Pi Day Teacher Resources

NASA Jet Propulsion Labratory | Oh the Places We Go: 18 Ways NASA uses Pi

NASA | STEM Lessons for Educators | Pi Day Challenge Lessons