Happy Pi Day

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Today is March 14, 2019. If we write it out as 3.14.2019, the month and day look like pi, a mathematical constant that denotes the circumference of a circle to its diameter. I believe this offers us an excellent opportunity to illustrate how superior fractional math is compared to decimal math.

Decimal math works fine when working with numbers that don’t have long running decimals, but sometimes we have decimals that never end. For example, one half translates to 0.5, which is easy to work with, but one third works out to 0.3333333333… the threes trail off infinitely off the end, even though 1/3rd of something is a finite thing. The same issue arises when we consider 2/3, which works out to 0.666666…, and 8/9, which is 0.8888888…eventually, we have to pick a digit and round off, which can ultimately result in a small rounding error. The more numbers we have with never-ending decimals in our calculation, the greater this error can grow. The trick in decimal math is to keep as many digits as possible to minimize the inevitable rounding error; but why bother? Why not just use fractions and eliminate the rounding errors all together?

In one of my finals in advanced trade school, the final big question on the exam was solving for a fairly complex parallel circuit, and the provided values would result in widely varying results depending on how many significant digits were used; so someone who rounded off after only two decimal places got a completely different answer than someone who rounded off at three decimal places, and neither would have been right. The “Correct” answer required at least six decimal places be kept throughout. I came up with an answer that was more accurate than the one on the answer sheet. Curious, the teacher wanted to know how many decimal places I went to. I told him, none; I just kept everything as fractions through to the end (every division problem is actually a fraction), and then simply converted the final fraction to decimal for the “Answer,” which I felt could have been better represented if left as a fraction as well, but sometimes we need a decimal number to work with at the end.

So, what does this have to do with Pi day? As a fraction, Pi can be represented as 355/113. If you convert this number to decimal, you will end up with Pi with an inhuman level of accuracy. To be sure, it’s not exactly Pi, at least to mathematicians who claim to know better, but the degree of accuracy is uncanny.

Back to Pi day, we can now see that 3.14 is a poor representation of pi. Perhaps there is another day that better represents pi, now that we understand the power of fractions when it comes to accuracy. If we go with a day-month-year format for our date, we can get a more accurate pi from 22/7. While not as accurate as 355/113, it’s still far more accurate than 3.14, and also provides a greater degree of accuracy than one would get from decimal math, from the same amount of numbers to memorize. In any case, maybe we should have two Pi days; one for decimal pi, and one for fraction pi, and let’s celebrate with some pie for our pie holes.

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