Estimating Pi Day

Today is pi day (3/14 – get it?), the not-exactly-official day to celebrate the mysteries of a circle’s circumference over its diameter.  When this most famous numerical expression of irrationality is closely combined with the second most famous irrational number –Euler’s constant, e – the result is a common mode of celebration today:  eating pie.  Enthusiasts pride themselves on memorizing pi’s non-repeating digits out to 100 places, or they put the first one million digits on their webpage.  Algorithms for calculating pi abound (my favorite requires a random number generator), with new ones regularly revealed.

But to use pi (π) in a calculation (which anyone who performs scientific or engineering calculations almost certainly will do), one must necessarily approximate by truncating pi to a certain number of digits.  One of the earliest truncations leads to just one digit:  the Bible equates pi with 3 in two verses.

1 Kings 7:23, New International Version: “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.” (2 Chronicles 4:2 says essentially the same thing.)

If you want to estimate pi to more than one digit, you must look to sources more authoritative than the Bible.

Modern politicians can be expected to do a bit better than a 2500-year-old religious text, but not by much.  In 1897, Taylor I. Record introduced a bill into the Indiana state legislature, written by physician and amateur mathematician Edwin J. Goodwin, which defined pi to be 3.2 (not even an accurate rounding).  The bill allowed Indiana schools to use Goodwin’s copyrighted proof of the squaring of the circle for free – schools from other states would have to pay a royalty.  The resulting House Bill 246 passed unanimously, 67 to 0.  Fortunately, the chair of Purdue University’s mathematics department, Professor Clarence Waldo, fought bravely against this injustice against enlightened thinking and empirical observation.  By lobbying the state Senate, Waldo convinced the Senators to table the bill indefinitely.  (For the complete story, see here.)

Alas, we still have too few scientists and engineers and mathematicians in elected office.  And while redefining pi is unlikely to come up again in legislation, there are still too many attempts to legislate the results of science, from evolution to climate change.  We will always need more Clarence Waldo’s preaching reason, and more legislators who will listen to them.