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Abstract

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.

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