Discovering Pi

We recently did an experiment to discover the value of pi. We did this well before Pi Day, and true to form, we are reporting on it after Pi Day.

Our first experiment measured pi by measuring the diameter and circumference of bean cans. We measured the diameter by putting a ruler across the can and measuring the biggest line across the can. We measured the circumference of the can by putting masking tape around the top of the can, marking the circumference on the tape, removing the tape, and measuring how long the tape was.

C's measurements were
diameter = 10.1 cm
circumference = 31.5 cm
and pi = c/d = 3.12

Sam's measurements were
diameter = 8.55 cm
circumference - 26.6 cm
and pi = 3.11

Not bad!

Our second experiment compared the weight of a square of cardboard to the weight of the circle it contained.



Dad did lots of explaining about ratios, density, and the formula for the area of a circle. After some fabulous and very interesting algebraic manipulation we found out that we could measure pi by comparing the weight of the square of cardboard to the weight of the inscribed circle:

pi = 4 x weight of circle/weight of square

We used a compass to make a circle on some cardboard. We drew a square around the circle using a plastic triangle. Then we cut out the square and weighed it on a junky old scale that has a broken unbreakable cover that covers the needle. The square weighed 1 5/8 ounces. Next we cut the corners off to make a circle and weighed the circle. The circle weighed 1 3/8 ounces. Using the formula above we calculated pi:

pi = 3.38

Not as good. We discussed why our first experiment gave us a better value for pi. C concluded that the ruler worked better than the scale, because the ruler actually works. Dad would like to note that it would be interesting to repeat part 2 with a heavier material or a more sensitive scale.