If you were paying very close attention last week, you’ll have noticed my attempt to come up with an estimate of π, geometrically, as part of The Aperiodical’s π Day challenge (even if it’s not really π Day):
Oo, my second effort at estimating π came to 3.14151, correct to 0.003%! cc @aperiodical pic.twitter.com/2vuvys0mka
— Colin Beveridge (@icecolbeveridge) March 10, 2015
Happy π day everyone! I hope you’re having a great day, and having lots of fun mathematical parties.
You may have noticed that here at The Aperiodical, we’ve been posting exciting π-related items all week – and here’s a list of them all, collected into one handy place. Enjoy!
It’s a tool; a ratio, providing us simple rules for doing circular estimates. Admired regularly – and we all remember that today’s pi! Hooray! Let’s eat pie.
You may have noticed that the first paragraph of this article was immensely poorly written, and didn’t sound like good writing at all. And you’d be right – except writing it wasn’t easy as you’d think. I’ve written it under a constraint – that is, I’ve picked an arbitrary rule to follow, and have had to choose my words carefully in order to do so.
In the excellent $\pi$ approximation video, Katie Steckles asked for $\pi$ approximations. I teach a first year techniques module (mostly calculus and a little complex numbers and linear algebra). This year I have changed a few bits in my module; in particular I gave some of my more numerical topics to the numerical methods module and took in return some of the more analytic bits from that module. This gives both modules greater coherence, but it means I have lost one of my favourite examples, from the Taylor series topic, which uses a Maclaurin series to approximate $\pi$.
They say that $\pi$ is everywhere. (They say that about $\phi$ too, but I’m not buying it.) I thought it would be interesting to discuss the most unexpected place I’m aware it’s ever appeared.
As part of our massive π day celebrations, The Aperiodical has challenged me with the task of assembling a group of mathematicians, some bits of cardboard and string, and a video camera, and attempting to determine the exact value of π, for your entertainment.
The challenge, which was to be completed without a calculator, involved using known mathematical formulae for π and its occurrence in the equations of certain physical systems. In the video below, seven different methods are used – some more effective than others…
If you reckon you too can ineptly compute a value in the region of π (in particular, if you can get a more accurate approximation than the date of π day itself, which gives 3.1415), feel free to join in the challenge and see how close you get.
People with an interest in date coincidences are probably already getting themselves slightly over-excited about the fact that this month will include what can only be described as Ultimate π Day. That is, on 14th March 2015, written under certain circumstances by some people as 3/14/15, we’ll be celebrating the closest that the date can conceivably get to the exact value of π (in that format).
Of course, sensible people would take this as an excuse to have a party, so here’s my top $\tau$ recommendations for having a π party on π day.