You're reading: Posts Tagged: approximation

Measuring π with a pendulum

 

Matt Parker approximating pi using a pie

Friends of the Aperiodical, nerd-comedy troupe Festival of the Spoken Nerd, are currently on tour around the UK. As part of their show, questionably titled You Can’t Polish a Nerd, Matt Parker attempts to calculate the value of $\pi$ using only a length of string and some meat encased in pastry. He’s previously done this on YouTube, and the idea was inspired by the Aperiodical’s 2015 Pi Approximation Challenge, and in particular my own attempt to approximate $\pi$ with a (more conventional) pendulum.

Ohioans measure a really big π

20160312_140500

Ohio State University mathematician Niles Johnson got in touch on Friday to tell us that our π Approximation Challenge last year had inspired him to hatch an audacious plan to measure a really big π.

The word ‘geometry’ is derived from the Greek for ‘measurement of land’, and Dr. Johnson took that quite literally: he wanted to measure the Great Circle Earthworks in Heath, Ohio; a part of the Newark Earthworks (not their original name) built over 2,000 years ago.

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 $\pi$.

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.

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.)