## You're reading: Posts Tagged: approximation of pi

### Ohioans measure a really big π

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.

### I bought three.onefouronefivenine.com

I’m a big fan of novelty domain names: I once bought hotmathematicians.com just so that christian@hotmathematicians.com could be my corresponding address when I submitted a paper. That domain has expired, but my love for one-shot novelty purchases has not!

To celebrate π day this year, I decided that it should be possible to type a little bit of π into the internet and be given the rest of it. You can have dots in domain names, so a domain like “three.something.com” is possible. I only know π to two decimal places off the top of my head, so I was dismayed to learn that onefour.com is being squatted.

After a bit of googling to find more digits of π (hey, this website will be really useful once I set it up!), I found the first decimal approximation which hasn’t already been registered:

### three.onefouronefivenine.com

Try going there now. It really exists!

I’ve set it up so you get an endlessly scrolling list of decimal digits of π, generated using my favourite unbounded spigot algorithm. I suppose you can consider this my entry in our π approximation challenge.

A good π day’s work.

### 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 $\pi$.

### Matt Parker approximates π by weighing a circle

Stand-up mathematician Matt Parker has accepted our π approximation challenge. His method involves weighing a large cardboard circle.

So, how did that go? Fortunately, Matt got it all on video:

I think he deserves a round of applause for doing all that long division.

### π, Phase Space, and Bouncing Billiard Balls

There are many ways to estimate or calculate π, that number that is irrational, but well-rounded. But perhaps none is as remarkable as that outlined in a 2013 paper by G. Galperin. In this brief article we’ll have a look at the problem, and see the setting, although we’ll leave the interested reader to hunt down the details.

### 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.