02(02): Pi day

Today is March 14, which can be written as 3/14, and these digits correspond to the first 3 digits of the mathematical constant which is defined as the ratio of the circumference of a circle to its diameter, at least in the decimal system that we human beings have arbitrarily chosen to adopt.

π is one of the first mathematical constants to whom an elementary learner of mathematics would be introduced. Most people should be able to at least recall that it has something to do with a circle, and most probably would at least know the first three digits of this constant.

π is an irrational number, and what that implies is that cannot be expressed as a ratio of two integers. That’s why it is called “ir-rational” (i.e. no ratio). What this means is that you can’t find a nice recurring pattern in its decimal expansion. This is contrasted with a popular approximation of π: 22/7, whose decimal expansion is 3. 142857 142857…

Notice how the group of digits ‘142857’ repeat.

In an article published exactly five years ago (Hickey 2015), a ‘SurveyMonkey Audience’ was asked to put a poll to see how far people could get reciting the infinite digits of pi. Of 941 respondents, 836 attempted to name the digits after the decimal point. Here is an extract from that article:

Interesting.

3. 14159 26535 89793 23846 26433 83279 50288 41971

That’s what I can recall from memory. 40 decimal places. I chose this number of digits to memorise a long time ago because with this number of digits, one can calculate the circumference of the observable universe to an accuracy of a hydrogen atom. Of course, when I decided to learn it, I didn’t expect to have to use it at all. It was mostly just for fun.

The unbelievable thing was that two years ago, when I participated in a freshman orientation activity, I remember that one of the station activities required that our somebody within our group recite the first 20 elements of the Periodic Table and write the first 12 decimal places of π with our short-term memory after trying to memorise it. It goes without saying that I certainly helped my group out in the latter exercise!

NL
14 March 2020

References
HICKEY, W. 2015. Available: https://fivethirtyeight.com/features/how-many-digits-of-pi-you-have-to-have-memorized-to-be-special/ [Accessed].

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