Wednesday, March 14, 2012

14th March: Pi Day, A Legend's Birthday and Buffon Matches

A blogpost on the 14th day of the 3rd month of every year, every earthling knows it as 14th March, but look closely at the three digits -3,1,4 and they turn out to be the most significant digits of Pi, the most famous of mathematical constants. 

Today is Pi day.

Yeah, not that. 

 More like it.

Back to Pi business. 3/14 (in the month/date format) is popularly commemorated as Pi day, because, well, the first three digits of π are 3,1 and 4. The Tau proponents have their own day, 28th June, and would rather call 14th March as half-pi day. But that's another story.

Other than eating pi pies, like the one in the picture above and having discussions on pi, this day has no other special significance. Some people like memorizing digits of pi (one chap has gone beyond 50000 digits also!), while others make their own mnemonics, or indulge in Piphilology.

Besides being Pi day, 14th March is also the birth date of the omnifamous Albert Einstein. Lets sing him Happy Birthday!

This blogpost rounds up some web media that I stumbled upon, which is both interesting and related to Pi and Pi Day.

Digits of Pi - the Abstruse Goose way! 

Google had its own Pi Day doodle two years back, as opposed to this year, when the doodle is on Origami Master Akira Yoshizawa's 101st birthday!

Pi is an important constant as it appears everywhere - from moving bodies to celestial objects to geometry. This is because pretty much everything in Nature has circles to it, because a circle is the most elementary shape there is. This is a link to an article which tells more...

Here is a Pi Clock that you can use to decorate your room!

Here, Pi has been used to denote the angle which the minute hand has taken as it goes round the clock, in radians. 2π radians is 360 degrees, which means the minute hand has gone one full circle, which means its now at 12. 

Some of the Intelligent YouTube channels I subscribe to were abuzz with activity yesterday, with Numberphile (a channel on Math & Number Theory) uploading as many as 4 videos on Pi. Meanwhile, MinutePhysics, of course a Physics based channel, uploaded a video summarising Einstein's great works on the great man's birthday!

Below are links to Numberphile's videos, which require about half an hour of viewing. The last video on Buffon's Matches really got me excited, so I decided to replicate the experiment on my own and embed the video! Also embedded is the video on Sounds of Pi - something else that I found interesting as it combines music and mathematics. 

1. Some Stuff about Pi

If you notice, this video has a runtime of 2π minutes!!!

Again, this video has a runtime of 2π minutes! Still skeptical about the random nature of the experiment and the result of somehow obtaining π from such a random experiment, I decided to replicate this, with strips of paper rolled up into cylindrical sticks. I did this three tims with 50, 64 and 80 sticks of paper, and got 3.125, 3.2 and 3.2 again! Given a larger, or maybe infinite sample, one will certainly get Pi! Although the explanation of this Buffon's Needle problem required calculus and so was beyond my understanding, it does have something to do with probabilities and the different angles at which a match can land between two lines! In fact, in 1901, Italian mathematician Mario Lazzarini performed an experiment using 3408 needles and obtained a result close to π. But, this result was too close, rather is was exactly 355/113, and it appears that he used some form of trickery in his experiment.

FlippyCat - one of the most popular domino toppler youtuber, gave this video as a tribute to Pi last year.

On a lighter note, the channel Asian Glow produced a spoof of you-know-who's popular song Friday, and made it Pi Day!!!

Here is the official Pi Day website of Exploratorium, whose faculty physicist Larry Shaw introduced the concept of Pi Day in 1988.

Pi is known to be an irrational, transcendental number, which means that it cannot be expressed as a fraction like 22/7 and that it has infinitely many digits in the decimal place, which means that there is a finite probability that you may find your cell phone number in the digits of Pi! This also means that no algebraic operation on integers can ever give you Pi as your answer, which raises an important question - How do you then determine the value of Pi, when you cannot perform an algebraic operation to yield Pi as your answer?

The answer is infinitely continuing expressions. The values given by these expressions fluctuate alternately - so for one expression the answer might be above Pi and for the next one the answer might be below Pi. The point is that, only if the series is continued infinitely can we get an exact value of Pi. Or you can use approximations for Pi which need not be infinite, but then, you end up with only an approximate value. Infinite Series have been indeed very helpful - especially those made by Indian mathematician Srinivasa Ramanujan (the infinite series are available on the internet, but I didn't put them here because they were too hairy :P) - and today we know the value of Pi to about 10 trillion decimal places!

Here are the first 1 million digits of Pi - try finding something inside them - something like your phone number, credit card number, or just try finding other important or random numbers in them!

You can make a "Pi Search" here -

In the first million digits - each of the numbers - 111111, 222222, 333333..... 888888 occurs once in the sequence, but 999999 occurs 2 times! Also, the first six digits of the square root of two - 1.41421 occur once in order in the decimal representation of Pi. I even found out the digits of my friend's phone number in them! Remember, theoretically, you can find anything in there, given infinite digits of Pi!

Remember the two occurrences of 999999 that I told you about? The first sequence of six 9s begins at the 762nd decimal place - which is considered very rare - because the digits from 0 to 9 occur almost with the same frequency among the first million digits of Pi - and the probability of six 9s occuring this early in the decimal representation is only 0.08%

This point is also called Feynman Point - after Richard Feynman (my fav physicist) who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip "nine nine nine nine nine nine and so on", suggesting, in a tongue-in-cheek manner, that Pi is rational!

And lastly, here is a mnemonic, no, a Piphilology (a pun on Pi itself and the linguistic field of Philology) to remember the first 15 digits of Pi. The length of the word (in letters) corresponds to that digit of Pi.

How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. 


If you are really serious, and want to go further in your quest to memorize the digits of Pi - the Cadaeic Cadenza, a short story written in Pilish by Mike Keith in 1996, will help you go on to 3834 digits. But the longest text written in standard Pilish is Not A Wake: A Dream Embodying π's Digits Fully For 10000 Decimals, a book written by Mike Keith again. 

Hope all that Pi-led up and amazed you. If you want to share any other interesting Pi-ish information, you may do in the comments section below! 

Till then, Happy Pi Day!

In tribute to Pi, a ubiquitous, simple ratio that is irrational and transcendental, feels amazing to write down and equals three point one four one five nine two and so on...