Today, March 14, is π Day. This stems from the fact that, in the US, March 14 is abbreviated as 3/14, matching the first three digits of π, 3.14…

Indeed, this is a very special π day that happens only once per century. Since it’s 2015, today is 3/14/15, matching up not just the first three digits of π, but the first five: 3.1415…

If you want to go completely crazy, check back in at 3/14/15 9:26:53 AM or PM. Here we have the first ten digits of π: 3.141592653…

Despite all this, and despite the fact that I love maths and the number

π

in particular, I’m not overly excited.

## Different bases

Writing out 3.141592653… is just one possible representation of π. In particular, it’s the beginning of the decimal, or base 10, representation. But this is not the only possible way to represent π.

The number system most commonly used in the modern world is the decimal system, based on powers of ten. The rightmost digit in a number is the ones (10^{0}) place, the next digit to the left is the tens (10^{1}) place, the third digit is the hundreds (10^{2}) place, and so on. For fractions or irrational numbers like π, we use places to the right of a decimal point to represent powers of 1/10: the first digit to the right of the decimal is the one-tenths place, the second is the one-hundredths, and so on.

But ten, and so the decimal representation of π we’re celebrating today, is an arbitrary choice. We use decimal largely because most humans have ten fingers. If we had eight fingers, we’d probably all be using octal, or base 8 instead: The rightmost digit, ranging from 0 to 7, would still represent ones (8^{0}), but then the digit to the left of that would represent eights (8^{1}), the next digit 64’s (8^{2}), and the fourth digit 512’s (8^{3}).

We can write π in whatever base we like, as shown on this handy website. In our base 8 world where we had four fingers on each hand, we would instead write π as 3.1103755242…

Assuming that the calendar in base 8 world is somewhat similar to our own, we’d celebrate π day on March 11, or 3/11. Note that this would be the ninth day of March: 11 in base 8 represents 1×8 + 1×1 = 9 in our decimal system.

That arbitrary nature of the particular representation of π in base 10 is why I can’t get overly excited about π day. March 14 is only celebrated as π day because of the number system we happen to use. Change our number system, and you change π day. Given that π shows up in nearly every branch of maths and science and is one of the most fundamental numbers in our universe, a day for celebrating this amazing constant shouldn’t be so ephemeral and randomly chosen.

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