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How Ultimate is Ultimate π day?

This year, π day will be celebrated, as always, on 14th March. Unlike most years, π day will be more accurate than usual – owing to the fact that the year, 2015, will give the date 3/14/15 (provided you’re using a US calendar date format) – and for this reason, some people are calling it Ultimate π day. But how truly Ultimate is it?

Now, don’t get me started on the ludicrousness of using the MM/DD/YY date format (or in this case, the M/DD/YY format as it’s most convenient to exclude the leading zero) — I personally favour YYMMDD, which means when I use it to log when I created a file, I can sort by name and get them in date order, but then I am a bit of a traditionalist in that sense — but, provided you’re willing to concede that it’s probably the best one to use in this case, π day is doing pretty well this year. I mean, given that there’s no such thing as the 31st of April (something I’ll always be sad about), it’s the best we’ve got.

In the UK, it’s more traditional among sticklers to celebrate π Approximation Day, which falls on 22/7 (or if you’re in the US, 7/22 for some reason). This gives a value of π of 3.142857… which, at a distance of 0.00126… away from π, is actually closer than π day’s usual effort, 3.14, which is 0.00159… away. This year though, we’re 3.1415, which is obviously much nearer.

But is this the best we can do? Given how arbitrary the decisions involved in choosing the calendar are, surely as mathematical nerds we can work out a closer value?

One easy way to add ‘precision’ is to use not just days, but instants of celebration – so, on π day this year, you could for instance throw a second-long party at 9:26:53, and then you’ve got a bunch more digits. Of course, real π enthusiasts would build themselves a time machine, travel back 423 years and deeply enjoy the instant at 6:53:58 on 3/14/1592.

I’d be interested to know what it was like back then – did people understand maths well enough to celebrate π day? We hadn’t yet managed to establish even 20 digits of π for sure, and those known had been obtained by inscribing polygons in a circle. A rudimentary form of calculus had been invented by a school mathematician in India, although it’d be around another 100 years before Newton published his version. π was certainly known, but it had only been that century when Arabic (modern) numerals had surpassed Roman numerals as the fashionable way of writing numbers.

On the Wikipedia page for 1592, Ultimate π day is listed as having taken place – but then so is “English explorer John Davis, […] , probably discovers the Falkland Islands.” So maybe our grasp of the actual events back then was slightly fuzzy; perhaps we’ll never know what those parties were like.

But I think we can do better. If we’re talking individual seconds, surely your best method of measuring time is using Unix time. Unix is an operating system that inspired Linux and several other computer operating systems, and is favoured by proper nerds as the correct thing to run your computer on.

Also known as “Epoch time”, Unix time is measured as the number of seconds that have elapsed since the beginning of the international standard UTC (Coordinated Universal Time), which was at midnight on 1st Jan 1970. As I write, it’s 1425850779 in Unix time; if you’d like to find out what the Unix time is, and you’re using a Unix based computer, you can always type date +%s in the terminal to find out (or you can go to Interestingly, Unix time struggles with incorporating leap seconds, and has to do a strange dance in order to accommodate them, meaning that e.g. 915148800.50 happened twice.

This form of storing the exact date and time is used by Unix-based operating systems and many file formats, and of course offers us many opportunities to look for approximations to π.

The first of these will have happened at 00:00:03 on 1/1/70, then another at 00:00:31, then after 314 seconds had elapsed, then after 3141 seconds, and so on. Each of these times would have taken ten-and-a-bit times as long to reach as the previous one did, so once we passed the time 31415926 (on 30th December 1970, roughly a year after the start of Unix time), the next one would have been around ten years from the start date, then a hundred years more to the one after that.

And in fact, because we started in 1970, the date 314159265 was in the early hours of 16th December 1979, and the next, 3141592653, won’t be until 21st July 2069. If you can wait that long, that’s surely the best π moment we could wish for in our lifetimes.

But what about other calendar systems? The Mesoamerican/Mayan Long Count calendar, which famously ‘predicted’ the end of the world in 2012, uses a different base system than decimal. It’s a curious mixture of base-20 and base-18, as below:

mayan calendar example

This is the date of π day, written in Mayan Long Count. It’s measured as the number of days since 11th August, 3114 BC (the day they started counting); the base system uses ones in the right hand column, and 20s in the next column, as you would for base-20, but the second column only counts up to 18. That means the next column is not 400s (as it would be in base-20) but 360s, followed by 7200s and 144000s. π day this year is 1872813 days since the start of the calendar, and the image above shows how this number is written. If you’d like to play with the Mayan calendar yourself, an online converter is useful.

So, can we work out which day is going to be the π-iest? Well, how about this one?

mayan calendar pi day

This represents $3 \times 144000 + 14 \times 7200 + 15 \times 360 + 9 \times 20 + 2$ days after the start of the Mayan calendar, which would be (according to my back-of-an-envelope calculations) September 9th, 1640BC. So, we missed that one. The next one to try would involve using the next column, and each digit in that column represents around 7886 years, so putting a 3 there would mean we’re well in the future and not likely to reach it while the human race still exists.

So maybe there’s another way to have π day, much closer to home. π is of course, a letter in the Greek alphabet, and since in this country certainly we abbreviate the days of the week to M, T, W, T, F, S, S, here’s a suggestion. Friday is known in Greek as παρασκευή (Paraskevi), which we could quite happily abbreviate to ‘π’. So we can celebrate an extremely accurate π day (giving exactly π), every week! (Although, for completeness, I feel compelled to point out that the Greek word for Thursday, πέμπτη (Pémpti), also begins with a π, so in Greece there’s two π days every week. Talk about spoilt!)

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$\LaTeX$: You can use LaTeX in your comments. e.g. $ e^{\pi i} $ for inline maths; \[ e^{\pi i} \] for display-mode (on its own line) maths.

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