Measuring the circumference and diameter of objects, such as coins and lids, allows students to discover pi (𝛑) from the circumference-to-diameter ratio. From multiple measurements of these two variables and the calculation of the simple ratio, measurement variation can be examined in a variety of numerical and graphical approaches, plus the influence of both random and systematic errors can be explored and percent error using the known value of pi. A best-fit mathematical model can be examined where a plot of circumference as a function of diameter yields the value of pi from its slope. By using a common US standard object (4-inch PVC pipe connector), the accuracy and precision of the measurements can be evaluated. Additionally, utilizing a pre-built Google Sheets spreadsheet (https://goo.gl/oYVQzS), data is collected, graphs produced, and computations performed in a shared environment in the cloud via Google Drive. This allows online collaboration and comparison within the class and between classes and even institutions, all-the-while building a large data set. Since the diameter measurement requires measuring through the center of the object, the diameter measurements could be underestimated which would yield a positive percent error in the determination of pi by this method. Random error should also be minimized as the number of objects measured (sample size) increases as well.
Sinex, Scott A. and Chambers, Theodore L.
Discovering Pi and its Measurement Variation: A Collaborative Cloud Activity,
Spreadsheets in Education (eJSiE):
3, Article 4.
Available at: http://epublications.bond.edu.au/ejsie/vol10/iss3/4