The beauty of irrationality

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By John Pawlak

There once was a number called pi.  So special like e and like phi.  The circumference to D is the ratio for me.  And it’s not a multiple of i.”
You really have to love mathematics to admire the symmetry of math poems.  This particular one is known as a pi-poem, or a piem.  Some people use the word piem to refer to a haiku-like poem of 3 lines with 3 syllables, 1 syllable, and 4 syllables.  Or if you wish, you can simply write a standard haiku about pi and call it a piku.
Does math really merit a poetic presence in our world?  Consider a typical math problem:  Given that four black cows and three brown cows give as much milk in five days as three black cows and five brown cows give in four days, then if the farmer gets really hungry, which cows should he eat first?
Okay, math questions usually don’t give students the opportunity to apply algebraic concepts to dietary situations like that.  More often, it’s something much more dull like “What’s the ten millionth digit of pi?”  Or a more typical question; What’s 7 times 8?  Well, it’s the same thing as it was yesterday and very likely won’t change next week either.  How many times do we have to ask the same question?
That is, of course, the nature of mathematics.  Mountains of mathematics being scaled for the same reason people trek up Kilimanjaro, Everest, and Aconcagua.  Because it’s there!
It is with this mentality that we celebrate the advent of Pi-Day (March 14th).  At 1:59 p.m. (and 26 seconds), the date-time will be 3/14 1:59:26.
 You have a little more than a week left to start memorizing pi to impress your friends.  The quest for pi, pi, and more pi, seems to get more irrational every year.  Ah, some of you caught that little pun, eh?  Pi is in fact an irrational number (one of the few math vocabulary words that makes sense to society).  Like my columns, it goes on and on forever without ever showing any real pattern.
 The challenge to conquer pi bubbles up every March and already I have students who have been working at memorizing it out fifty places. Of course, my offer of rewarding them with a pie for pi might be just the sweet motivation required, but you do have to wonder why others out there keep striving to break the record.  The current world champion is Chao Lu who recited pi out 67,890 places.  It took him 24 hours 4 minutes to spew out a stream of digits that if printed in this newspaper would be 410 feet long.
 The history of pi is more interesting that pi itself.  Some 2000 years BC, the Egyptians used 3.125 to estimate pi.  Even the Mesopotanians used 3.162, not a bad approximation for a culture than used a base-60 system.
The Greek astronomer, Ptolemy, was totally off base with his geocentric model of the solar system.  He did however calculate pi out to four digits in 150AD.  Jamshid al-Kashi, an Islamic mathematician, calculated pi out an astonishing 16 digits in 1430 AD.  And William Shanks of England managed to beat that in 1873 by manually calculating pi out 527 places!
As people throughout the centuries kept straining brains to go one digit further, computers eventually trumped the imagination by computing pi out to lengths that truly stagger the imagination.  Using a home PC and an algorithm developed by a Northwestern University grad student, a Japanese man calculated pi out ten trillion (10,000,000,000,000) digits.  Reciting this number one digit per second would take over 300,000 years.
 So okay, maybe you won’t be breaking any pi records this year.  But you can at least do better better than Ptolemy.  3.1415926 - that should be accurate enough for your GPS to get you to where you’re going.
By the way, for those who are truly mathomasochistic, the ten millionth digit of pi is “7.”
And for those who appreciate the realities of probability, what do you think the chances are that I looked that up on the Internet?
 John Pawlak
Los Alamos Columnist