9. The Value of Pi

Wouldn’t it be great to lay out a huge circle in some open field, measure the diameter and circumference (string or rope would have to be laid along the circle first), and see how close we get to the value of π? School children should do this at least once in their K-8 years.

Students are often asked to evaluate C/d for “round” objects they could find around the house. While the first decimal place can usually be attained, it is pretty difficult to get the second decimal place correct. Inaccuracies typically arise because students attempt to surround the object with a tape measure (too stiff, a cloth measure is better, but still not easy), or to roll the object one complete revolution along a straight line (it will almost always slip). Probably the best suggestion is to surround the object with masking tape (never surround it with anything elastic). It forms a nice fit; it can be well marked, and then cut and straightened to get a good measurement of the circumference. Students must also remember that the diameter is generally the “outer” diameter (because that is what the making tape extends to). This will produce good results, but it would be great to go outside and make a really large circle.

It is worth pointing out that this MathLab (i.e., optimally, going outside and making a large circle) regards the actual definition of π (π = C/d). Activities such as folding a circle, cutting it, and “almost” forming a parallelogram (or rectangle) to determine its area (which is then compared to the circle area formula A = πr^2) is a nice activity for approximating π via an indirect means, but generally can be performed in class or as an ordinary assignment.

Here,

Q. The question is simply, “What is the ratio C/d of the circumference C of a circle to the circle’s diameter d?”

R. The answer is provided by actually measuring, as finely as possible, the circumference and diameter of as good (and as large!) a circle as possible.

V. Of course, the value of π (a transcendental irrational number beginning in 3.14159265…) is known today to over a trillion decimal places, by way of analytical means. So, the results can be judged immediately.

Collaborative School Activities for the Teaching and Learning of Mathematics