Since it’s $\tau$ Day, we thought we’d give Festival of the Spoken Nerd constant-fans Matt Parker and Steve Mould a chance to air their respective viewpoints in the $\tau$ vs $\pi$ debate. It’s a maths showdown!
Something that whipped round Twitter over the weekend is an early version of a paper by Francisco Aragón Artacho, David Bailey, Jonathan Borwein and Peter Borwein, investigating the usefulness of planar walks on the digits of real numbers as a way of measuring their randomness.
A million step walk on the concatenation of the base 10 digits of the prime numbers, converted to base 4
A problem with real numbers is to decide whether their digits (in whatever base) are “random” or not. As always, a strict definition of randomness is up to either the individual or the enlightened metaphysicist, but one definition of randomness is normality – every finite string of digits occurs with uniform asymptotic frequency in the decimal (or octal or whatever) representation of the number. Not many results on this subject exist, so people try visual tools to see what randomness looks like, comparing potentially normal numbers like $\pi$ with pseudorandom and non-random numbers. In fact, the (very old) question of whether $\pi$ is normal was one of the main motivators for this study.
People celebrate today as “π day“, an official designation in the US*
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…
A new post is available over at Second-Rate Minds by Peter Rowlett.
How would you calculate ? I remember being sent as a boy of ten into the schoolyard to find circular objects to measure. Our attempts to wrap a tape around a dustbin lid clearly did not represent the optimal method. Perhaps you know a few digits of . Starting from scratch, how would you find …
Read the full post: “How to calculate π“
Today I spent an enjoyable time at Pi-hunting – the story of a mathematical obsession, run by the British Society for the History of Mathematics (BSHM) at the British Science Festival 2010.
Part of this included a presentation by Noel-Ann Bradshaw on mnemonics to remember the digits of pi. An example is the following:
How I wish I could calculate pi.
Look at the number of digits in each word in this sentence. The first word has 3 letters, the second 1, the third 4, and so on. It makes 3141592, the first seven digits of pi. Another example given, faithfully and quickly recorded by Mary Perkins:
How I like a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
There are longer versions including some which are much longer; for example this story encodes the first 740 digits. This is more an example of constrained writing than a useful mnemonic.
Noel-Ann raised the challenge to the audience to come up with their own and so I thought I’d pass this on to you. On the train on the way home I had a go at a tweet-length version (ignore punctuation, including the #):
Now I away,
I leave enlivened by having great and happy
historic, enjoyable, happily unanimous joy
at the exciting BSHM #pihunt
This is topical, although I’m not sure how well it might help you remember pi, but I think we’ve lost track of that original point, haven’t we?
So you can leave yours in a comment below or, even better, why not tweet it using the hashtag #pihunt. This can be any length, just stop at the number of digits that suits you. To help, just in case you can’t remember them all, here are some digits of pi: