Measuring The constant is defined to be the ratio of the circumference to the diameter of a circle. One should be able to determine the value of therefore, by measuring the circumference and diameter of a circle, and dividing. How well does this work in practice?

Suggestions:

You might consider using some cylindrical objects instead of drawn-on-paper circles. If so, a (not the, a) way to measure the circumference would be to mark a dot on the cylinder, place the cylinder on a piece of paper with the dot on a line, roll it across a sheet of paper (without slipping).until the dot again contacts the paper. Alternatively, you could wrap a piece of tape around the object and mark the overlap...

Certainly, you would want to measure several cylinders of various sizes, right?

Be sure to carefully consider what measuring instrument(s) (meter stick, ruler, measuring tape, vernier caliper, micrometer caliper, etc.) is appropriate for your situation. Remember to record (in an appropriate data table) not just the measurement, but how it was made, along with an estimate of its precision, in your lab book.

Remember that your lab book is to be a complete, as-it-happens record of your experiment.

Results:

Of course, we all know that has a well-known value (calculated to at least a few million decimal places...). The mean value (see below) of your measurements would be the logical choice for your best estimate of the value of . Also, the standard deviation of the mean will give you an uncertainty estimate for your value of .

Time permitting (check with your teacher), it might be interesting to combine the results of all of the lab groups in the class to get a class estimate of .

Conclusions:

Well, how do your results compare with the mathematical value of ? How does the class value (if it was calculated) compare to yours?

Statistics using Excel and the TI-89

Here's how to calculate statistics you need using Excel:

• The mean value for the cells from A2 to A12 (inclusive0 is "=AVERAGE(A2:A12)".
• The standard deviation of the values from cells A2 to A12 is "=STDEV(A2:A12)".
• The standard deviation of the mean (SDOM) of the values from cells A2 to A12 is "=STDEV(A2_A12)/COUNT(A2/A12)"

You can type the function directly into a cell, or select it from the dialog displayed when you select "Function..." from the Insert menu.

If you are using the TI-89, click here for a short tutorial. If you are using some other calculator, consult the manual.

last update August 14, 2007 by JL Stanbrough