Saturday, 14 March 2009

Happy Pi day!!!

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806…ad infinitum

Yes folks! Today is March 14 (3.14), or, if you didn’t know, Pi (π) day.

Simply put, π is how many times ANY circle's diameter will wind round its circumference, that is π =C/D. But it’s much, much more than that. And it’s amazing how many common traits π shares with us.

We are not very good, for example, at making sound judgments: just look at what the idiotic bankers did and the collapse in share prices. But although π may not be responsible for the nonsensical movements in stock prices, it is also not rational because it is an irrational number (since it can never be expressed exactly as a fraction m/n).

And like humans, π shares a fascination with the divine. However, Pi is most definitely NOT a Christian. Why not? Well because the Bible uses an incorrect value for Pi of 3! How do I know this? Simple: just look at I Kings 7,23:

And he made a molten sea, ten cubits from one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (PI = 30/10 =3)

But while π may not follow a particular religion, it is nonetheless a transcendental number since no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can ever be equal to its value.

And as we behave in unpredictable ways, so does π. Amazingly, the sequence of digits in π has passed all known tests for randomness (even though there is no zero in the first 31 digits of Pi).

But it’s unfair to say that π lives in a mathematical world of its own. It doesn’t. In fact, it’s probably a lot more environmentally aware than we are. In fact, nature wouldn’t even exist without π, but it would without us.

So where can you see π? Well how about in equations that explain rainbows, ripples spreading from where a raindrop fell into water, superstrings, general relativity, normal distribution, the distribution of primes, geometry problems, waves, and navigation. And that’s just for a start!

So give π the respect it deserves. Happy Pi day!!

Some other Interesting facts on Pi (gathered from various sources):

1) Write the letters of the English alphabet, in capitals, clockwise around a circle, and cross-out the letters that have right-left symmetry, A, H, I, M, etc. The letters that remain group themselves in sets of 3, 1, 4, 1, 6"

2) The sequence 314159 re-appears in the decimal expansion of Pi at place 176451. This sequence appears 7 times in the first 10 million places (not including right at the start)

3) In binary Pi is: 11.0010010000111111011010101000100010000101101000110000100011010011…

You can do lots more stuff with Pi when it is in binary format - like drawing weird pictures of it, or even listening to it. As Pi has an infinite number of places, it is quite possible that any message you liked could be heard somewhere in Pi. It has even been suggested it contains the VOICE OF GOD. In Carl Sagan's book 'Contact' the places of Pi are found to contain a message from the beings that built the universe.

4) Daniel Tammet, a prodigious savant, once recited Pi to 22,514 decimal points in five hours and nine minutes!

5) There is a book called Cadaeic Cadenza by Mike Keith. In the 3834-word story each word in sequence has the same number of letters as the corresponding digit in Pi. The first stanza is:


A Poem

A Raven

"Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore". "


wankongyew said...

What? You gave honour to Pi Day but not Sqrt() Day? (03/03/09)

The Sycologist said...

oops - i missed that one, maybe next year...

wankongyew said...

Fat chance of that, since there are only 9 of those every 100 years:

1/1/01, 2/2/04, 3/3/09, 4/4/16, 5/5/25, 6/6/36, 7/7/49, 8/8/64, 9/9/81

Next one's in 2016.