Calculate Pi Using a Pie

Pi is described as the ratio of a circle's circumference to its diameter. If you are unfamiliar with this definition, but know the formula for a circle's circumference (C=πd), the ratio can be easily derived by dividing both sides by d. This also means that the only thing you need to calculate the value of pi is a circle whose diameter and circumference you can measure. Fortunately, a very tasty circle to use for this purpose is a pie, which is coincidentally a homophone of pi. This makes the whole process more enjoyable and fun, making the link not only from circumference to diameter, but also from pie to pi. In the following Instructable, you will find out how to find the value of pi using a pie in 4 easy steps.

1. A circular pie of any size
2. Long ruler or measuring tape
3. Thick string (such as cotton twine)
4. Marker

Bake or buy a pie of your liking. There are no limits or requirements for the pie itself except that it has to be circular. I used a home-baked cherry pie for my calculations. Any size pie will work, seeing as pi is merely a ratio of a circle's circumference to its diameter (meaning that the value of pi will not change no matter the size of a given circle).

The diameter of your pie is the distance across it from edge to edge, passing through the center point. Align your ruler or measuring tape as centrally as possible over your pie and take note of the measurement. For my pie, the diameter was 10 inches (25.4 cm).

The circumference of your pie is the distance around the edge of the pie. To measure the circumference, there are three steps that need to be followed:

1:

Take your string and lay it around the outer edge of your pie, taking care to make it as circular and accurate as possible. Making an accurate circumference measurement is really important for getting an accurate result for the value of pi.

2:

Mark the wrapped-around string where it crosses the loose end of the string with a marker.

3:

Unwrap the string from your pie, and straighten it out along your measuring tape or ruler, taking care to work out any kinks but not stretch it out. Measure the distance between the mark and the loose end of the string to find your circumference. For my pie, the circumference came out to be a little more than 31.4 inches (about 79.8 cm).

Now, having found the circumference and diameter of your pie, you can calculate pi. Since the formula for circumference is 2πr, which can be rewritten as πd, where d is the diameter and r is the radius, pi can be expressed as C/d, where C is circumference and d is diameter (the operation between the equation is a simple division by d on both sides. Plug your own numbers into the formula, and behold the final answer. Your answer will likely not be exact, as human error and the imperfection of the geometry of baked goods do not help precise calculation. However, it should be pretty close to pi, illustrating the proportional relationship between a circle's diameter and its circumference. For me, it worked out just about perfectly, with a circumference of 31.4 inches and a diameter of 10 inches, which results in a calculation of 31.4/10=3.14! Perfect! (although not too precise).

The time has come to eat the pie. After intensive measurements have been performed and calculations meticulously executed, the moment everyone has really been waiting for has arrived. Celebrate pi, and enjoy your pie, and show that math can be very interesting, and very tasty as well. :)