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π approximation: Machin’s formula

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 $\pi$.

Mandelbrot’s bum is full of π

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.

Video: The Aperiodical’s π approximation challenge

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.

How I Wish I Could Celebrate Pi

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.

3.142: a π round-up

Pi pie by Robert Couse-Baker. Photo used under the CC-BY 2.0 license.

π pie by Robert Couse-Baker. Photo used under the CC-BY 2.0 licence.

‘Tis the season to celebrate the circle constant! Yes, that’s right: in some calendar systems using some date notation, the day and month coincide with the first three digits of π, and mathematicians all over the world are celebrating with thematic baked goods and the wearing of irrational t-shirts.

And the internet’s maths cohort isn’t far behind. Here’s a round-up (geddit – round?!) of some of our favourites. In case you were wondering, we at The Aperiodical hadn’t forgotten about π day – we’re just saving ourselves for next year, when we’ll celebrate the magnificent “3.14.15”, which will for once be more accurate to the value of π than π approximation day on 22/7. (Admittedly, for the last few years, 3.14.14 and so on have strictly been closer to π than 22/7. But this will be the first time you can include the year and feel like you’re doing it right.)

Not Mentioned on the Aperiodical this month, 21 August

Here are three things we noticed this month which didn’t get a proper write-up, due to thesis/Edinburgh fringe/holidays: a big proof, a fun maths book club, and a ridiculous bit of pi-related madhattery.