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π calculated to 31 trillion digits

This Pi Day, Emma Haruka Iwao has announced calculation of \(\pi\) to \( \pi \times 10^{13} = 31,\!415,\!926,\!535,\!897 \) digits, exceeding the previous record of 22 trillion digits set in November 2016.

This used y-cruncher, running Chudnovky’s algorithm. Chudnovky’s algorithm is \( \mathcal{O}(n(\log n)^3)\), making each record more impressive. In a blog post, Emma writes about the benefits of using a cloud cluster, saying the calculation ran on a virtual machine cluster, using

25 nodes for 111.8 days, or 2,795 machine-days (7.6 machine-years), during which time Google Cloud performed thousands of live migrations uninterrupted and with no impact on the calculation process.

Ways to access the digits and fun related bits and bobs are outlined in the blog post.

More information

Pi in the sky: Calculating a record-breaking 31.4 trillion digits of Archimedes’ constant on Google Cloud by Emma Haruka Iwao.

Emma Haruka Iwao smashes pi world record with Google help, BBC News.

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.

Happy π day

People celebrate today as “π day“, an official designation in the US*

3.141592653589793238462643383279502
88419716939937510582097494459230781
64062862089986280348253421170679821
48086513282306647093844609550582231
72535940812848111745028410270193852
110555964462294895493038196...5...

Do you know how we know those digits? If you’d like to find out, I’ve written a blog post over at Second-Rate Minds: “How to calculate π“.

* This is not necessarily the best day. “3.14” is a very crude approximation for π and translating 14th March into this number requires a month/day dating system. 22/7 gives 22nd July in day/month format and gives a slightly closer approximation for π: 3.142857… (3.14 is π-0.00159…, while 22/7 is π+0.00126…). Having said that, 14th March has the tantalising prospect of 1:59 and 2.65359… seconds giving an actual value of π… Perhaps we need a fourteenth month…

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