Today is pi approximation day! And - it's also my birthday! It's been approximately
23 years that I've gone on an approximately circular orbit around an approximately spherical
star on an approximate spherical planet... I could go on, but instead I'm going to give
you an approximate history of the approximation of pi!
[INTRO by Cristina de Manuel & Caro Waro]
I'm sure a lot of people are aware that the 14th of March is pi day, but fewer people
are aware that today, the 22nd of July, or 22 over 7, is pi approximation day, and it's
actually a better approximation of pi than pi day itself.
Well, that is, if you're not counting the years. Some people know that pi day of
2015 and 2016 were the closest approximations of pi in the century, and in fact if you're
counting years, 24% of the time pi day is a better approximation of pi, than pi approximation
day and those run from from the 4th to the 28th year of the century, so we've still got another
good 12 years of being able to celebrate pi as "actually closer to pi day".
But anyway, back to pi approximation, the approximation of pi goes back a very long time
The laziest approximation of pi is 3, and that goes to the Babylonians. In spite of
it being grossly inaccurate, it was actually very handy for making very quick calculations.
It really didn't take that long for them to be topped by the Egyptians in 1600BC who estimated
pi from the perimeter of an octagon, which came out to be 3.16.
The 22/7 that we're talking about today was actually the brainchild of Archimedes in 300BC.
He actually approximated this using a very similar technique to the Egyptians, but instead
of an octagon he used a 96-sided polygon, and it's actually a really good approximation
of pi - it's only 0.04% off its true value.
In 236, Liu Hiu found an even better approximation of pi, and in this case he used a fraction
that had 3 digits in the numerator and three digits in the denominator, and it's the most
accurate fraction of this type.
Chinese mathematics would stay ahead of the game of pi approximation for the next few
hundred years having estimated pi to 7 decimal places.
No significant advances were made on the pi front until the 14th Century, when Indian
mathematician Madhava de Sangamagrama discovered an infinite series for computing pi, which
he used to calculate pi to 11 decimal places. From this point onwards, being able to calculate
the largest number of decimal places of pi actually became a bit of a hobby for mathematicians
and they used a plethora of different algorithms, series, equations and polygons with increasingly
larger number of sides for this end.
A few honourable mentions go to Dutch mathematician Ludolph van Ceulen, who calculated pi to 35
decimal places and was so proud of this that he asked for it to be engraved on his tombstone.
Another person of note was William Shanks, who actually raised the bar pretty high in
1873 calculating pi to 707 decimal places. Unfortunately, only the first 527 were correct
in spite of him checking his work daily, a feat which actually took him 20 years.
The fastest algorithm we know for calculating the decimal places of pi comes from one of
my favourite mathematicians, Ramanujan, in 1910. And since computers came onto the scene,
we skyrocketed from under 1,000 decimal places of pi to over 100,000, and closing in on the
year 2000 we knew over 200 billion decimal places of pi! And to date, with the use of
even more powerful supercomputers and algorithms, we know 13.3 trillion digits of pi, a number
which is honestly, unimaginable!
And the eternal calculation of the closest approximation of pi is likely running right
now, pumping up that figure of digits to even larger and unfathomable quantities. And let's
hope they're all correct, because in the words of another really cool statistician, John
Tukey, "it's best to be approximately right than exactly wrong".
I really hope you had a bit of fun with this today, I certainly did. It's my birthday but
as soon as I can I'm going to get a blog out with even more pi related frivolities for
your enjoyment, as always, thank you so much for watching me and I'll see you in the next one!
[MUSIC:Thastor and Cryosleepkitten] [ART: Caro Waro & Cristina de Manuel]
[Scripting, Filming, Presenting, Editing: Inés Dawson]