Pi Day!

Pi Day is coming up again (3/14 as a US date). The number π is, of course, 3.14159265… Here are some possible activities for children:

  • Search for your birthday (or any other number) in the digits of π
  • Follow in the footsteps of Archimedes, showing that π is between 22/7 = 3.1429 and 223/71 = 3.1408.
  • Calculate 333/106 = 3.1415 and 355/113 = 3.1415929, which are better approximations than 22/7.
  • Measure the circumference and diameter of a round plate and divide. Use a ruler to measure the diameter and a strip of paper (afterwards measured with a ruler) for the circumference. For children who cannot yet divide, try to find a plate with diameter 7, 106, or 113.
  • Calculate π by measuring the area of a circle (most simply, with radius 10 or 100), using A = πr2. An easy way is to draw an appropriate circle on a sheet of graph paper.

You can also try estimating π using Buffon’s needle. You will need some toothpicks (or similar) of length k and some parallel lines (such as floorboards) a distance d apart (greater than or equal to k). Then the fraction of dropped toothpicks that touch or cross a line will be 2 k / (π d), or 2 / π if k = d. There is an explanation and simulator here (see also the picture below). And, of course, you can bake a celebratory pie and listen to Kate Bush singing π, mostly correctly!

This picture by McZusatz has 11 of 17 matches touching a line, suggesting the value of 2×17/11 = 3.1 for π (since k = d).

Actually, of course, π = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 … (digits in red are sung by Kate Bush, accurately, although some have said otherwise).


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