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Make a pi necklace

By David, 19 September 2019 Activity

Image of a person wearing a necklace

What do you notice about the pattern of the beads?

Written by Gabrielle Tramby and Rachel Fitzgerald

In this activity, you’ll turn a number into a necklace. Pi (π) is the name of the number you get when you divide the circumference (distance around the outside) of a circle by its diameter (distance across it). No matter how big or how small a circle is, the value of pi is always the same!

You will need

  • 1 large bead
  • Smaller beads in 10 different colours (about 15 beads of each colour)
  • String or elastic to thread beads on, about 70 cm long

A copy of the first 100+ digits of pi:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095…

What to do

  1. Nine piles of beads sorted into colour groups.Sort the smaller beads into colours, and then give each colour a number from 0 to 9. For example, blue beads could be 1, red beads could be 2, and so on.
  2. A bead threaded on a piece of string.Thread the string through the hole on the largest bead, and tie it so one end of the string is secure.
  3. A string of colourful beads.Using the digits of pi above, thread the beads onto the string in the order of the digits, so that after the big bead, you end up with different coloured beads that translate into the digits of pi.
  4. Keep going until you run out of beads.
  5. Tie the ends of the string together and trim loose ends, so you have a necklace.
  6. A string of colourful beads with one larger bead.What do you notice about the pattern of the beads?

What’s happening?

Pi is an amazing number – it goes on forever! It’s an irrational number, which means it cannot be defined as a fraction. Pi is approximately 3.14159 but it has an infinite number of decimal places. The latest calculations include more than 31 trillion digits!

What’s more, the digits that make up pi don’t seem to follow any pattern at all, but if you count how many times each digit is represented in the first 100 decimal places, you’ll find they all occur around the same number of times – between 8 and 14.

Pi in real life

Pi can be used to check the accuracy of a super computer. This is done by asking the computer to calculate millions of digits of pi, then confirming the results against known digits.

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