One Circular Math Activity for Pi Day

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Compass Times Two : image by Mike DeHaan

You need a compass to calculate pi. Image by Mike DeHaan

We celebrate Pi Day on March 14 as a pun of the first three digits in the value of pie: 3.14. The Greek letter ‘π’ represents pi, which is equal to the circumference divided by the diameter of a circle. We calculate pi by measuring circles – and demonstrate that the ratio of circumference to radius is a constant, regardless of the radius of the circle.

Materials Required for the Circular Pi Day Activity

The materials you’ll need for this circular Pi Day activity are:

  • Note paper or log book
  • A sheet of paper to mark and measure
  • A ruler with fine markings
  • A pencil
  • A compass
  • Scissors
  • Calculator

How to Calculate Pi from Circles

First, create a table to record your results. The columns should include the radius and diameter of each circle, two separate columns for the length of the circumference, and two columns for the calculated ratio for pi. You can also include columns for the differences from pi, or measurement errors.

  1. Start by drawing a straight line on the paper. Set the compass, then measure the distance between the point and pencil tip; that’s the radius.
  2. Next, mark a point on the line as the center of the first circle. Then set the compass point there and draw the circle. It’s wise to measure the radius of the circle again on the paper.
  3. Cut out the circle. Be careful not to trim the circle.
  4. Cut a very thin sliver from the outside of the circle, and another thin sliver from the paper where the circle was cut out. Measure the length of these slivers; each approximates the circumference of the circle.
  5. Write the numbers and do the math.  Remember that the radius is twice the diameter: C = π*d = 2*π*r. So you can calculate π = C/(2*r).
  6. Repeat the process with circles of different sizes. Since pi is the ratio of the circumference to the diameter, the value of pi does not change, regardless of the size of the circle.

It’s your choice whether to complete one circle to measure and calculate or to draw all circles before measuring and calculating.

Alternative Ways to Go in Circles on Pi Day

An alternative to using a compass to create paper circles is to start with actual wheels. Either tie a string around the wheel, or wrap a strip of paper around the wheel and then tape the paper to itself (not to the wheel). Then, cut the string or paper strip so you can measure it with a ruler.

It’s even simpler to use a measuring tape rather than a string; but measuring tapes do not usually have very fine markings.

Celebrating Pi Day

The number pi is extremely important to mathematics. Many people who struggle with math benefit from using physical objects; Pi activities such as the Buffon Needle Drop and simple ‘pi’ rolling activities that require you to manipulate tangible objects are helpful. The constant ratio, “pi,” then becomes a concrete reality rather than a mathematical abstraction.

Calculating pi becomes very memorable, and more enjoyable, if you can finish with Pi Day pie as dessert.

Resources

Smoller, Laura. The Amazing History of Pi. (2001). University of Arkansas at Little Rock. Accessed February 23, 2013.

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© Copyright 2013 Mike DeHaan, All rights Reserved. Written For: Decoded Science
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