Both faithful readers know that every year I celebrate March 14. That, of course is Pi ((∏) Day. The day gets its name from 3.14, the first three digits of the ratio of a circle’s circumference to its diameter.
But other than the fact that March 14 also happens to be Albert Einstein’s birthday, today, July 22, is just as important — maybe even a little more so.
Today is known (by all of us in the know) as Pi Approximation Day. The fraction 22/7 (22nd of July) has a value of 3.142857, so it has the same first three digits as Pi.
Actually both 3.14 and 22/7 are approximations of Pi, so both days should get at least equal credit and just be called “Pi Day.” In reality, 22/7 is closer to Pi than 3.14, so maybe July 22 should be the real Pi Day and March 14 be Pi Approximation Day.
I know I’ve talked about this before, but pi is important, so we should probably review…. Pi is irrational. That means the decimal expansion never ends and never repeats, so any number of decimal places we write out is an approximation. Mathematicians and purists say the exact number can written using just one symbol — ∏.
Naturally, the more decimal places we use makes any computation involving pi more precise. But how precise do we need to be? If pi is rounded to just the integer 3, the accuracy of the computation will be off by about 4.51%. So if we use the value of pi as 3 and compute the circumference of an object with a diameter of 100 feet, we will be off by 4 ½ feet. By using 3.14 as the value of pi, the accuracy will only be off by about ½ percent. If we use 3.14159 the accuracy is within 0.000084 percent.
Some people have memorized pi to thousands of decimal places — I’m not sure what the value of this exercise is except a personal challenge, but then again they may be in a quest for eternal truth or something like that.
So Pi Approximation Day will be a little subdued this year, but I hope you celebrate with as big a Pi Approximation Day party as circumstances allow.
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