Scientific techniques are used to take measurements in standardized ways and to control error and precision. Mathematical techniques are used to recognize relationships among the variables measured and to develop formulas and generalizations based on that real-world data. Complete the following:
Using a collection of three circular objects, rulers with inches and centimeters, and some string, derive a relationship between the diameter of a circle and its circumference.
Task:
After completing the given problem, write an essay (suggested length of 3-5 pages) in which you do the following:
A. Describe your problem-solving process, including the following:
1. Describe the measurement tools used.
2. Describe the data collection process. (Make sure to take measurements in both metric and traditional units.)
3. Explain how measurements are approximations.
4. Provide a table of the data collected for all three of the items measured.
5. Explain how differences in units affect precision.
B. Explain how to use the collected data to derive an experimental value for pi (i.e., a relationship between the diameter of a circle and its circumference).
C. Analyze the degree of error in your measurements and your experimental value of pi, using the known value of pi.
D. If you use sources, include all in-text citations.