Tuesday, March 14, 2006

Happy Pi Day

Iris and I wish everyone a happy π day.
π is the ratio of the circumference of a circle over its diameter. The most common way this is expressed is shown below.

c = &pi d

This really sunk in for me when my 5th grade teacher sent me out with a measuring tape and a notebook to measure the diameter and the circumference of every round object I could find in an hour.

When I returned, we divided each circumference by its corresponding diameter measurement. Some of the ratios were larger than &pi, some were smaller. When we summed all the circumferences and divided by the sum of all the diameters (taking an average--but I didn't know that yet), the ratio became very close to &pi .

Why was one of the ratios so different than the others? I did recall that the trash can was dented in on one side. I leave the rest as an exercise for the reader. ;-)

2 comments:

  1. Gage error was normally distributed?

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  2. I doubt it, but I didn't know what a normal distribution was back then. I attribute to the fact that some ratios were higher and lower than the actual &pi because I did not measure the diameter correctly. Possibly, some of the round objects were more elliptical (dented) and I only took one measurement.

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