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Thursday, March 14, 2013

National Pi Day

I know what you're thinking - National Pi Day already?  I haven't even got a Pi wreath on the door or bought any Pi-Day cards!  Well, before you get sucked into the glitter and glamour of National Pi Day, all its commercialism and hype, think for a moment what Pi Day represents.  What Pi Day means.

Pi, or π of course is the ratio of a circle's circumference to its diameter.  Archimedes gets the credit for discovering it around 250 BC, which is why it has a Greek name, but in all truth pi was there all the time.  The Chinese geometer Liu Hui also approximated pi, and used similar methods to Archimedes, but you never hear of him, do you?  The Pyramids of Giza, built 2000 years before Archimedes, have a ratio between the perimeter and height which is approximately equal to pi (even Archimedes was only able to approximate it).  Somewhat later manuscripts from Egypt and Babylon calculate pi to 3.1 and change. The Hebrew Bible implies the value of pi in a description of King Solomon's pool which had a diameter of ten cubits and a circumference of thirty.

Pi has found applications in trigonometry and geometry, but also such high-falutin branches of learning as thermodynamics and fractals.  The chief charm of pi, however, is the fact it's so handy for calculating circumferences of circles if you know the diameter, and vice-versa, which is something most of us find ourselves doing on a regular basis.  Thank you Archimedes or Liu Hui or whoever you were for deriving the approximate value of pi!  I've got this radius here but I'd never be able to guess the circumference without it!

But pi is more that just a workhorse of computation for us to use in our daily lives like Euler's Number or the Fibinacci Sequence, for pi is a transcendental number, meaning it cannot be expressed accurately as a ratio between two digits in a fraction.  This is why representing pi in decimal form yields an infinite string of digits that never ends and never falls into a repeating pattern.  Who doesn't recall that classic Pi-Day Carol:

Three point one four one five nine two,
Six five three five eight nine!
Seven nine three two three eight four six,
Two six four three three eight three...!

How our parents loved to make us sing that and watch us go through verse after verse until we passed out from exhaustion and oxygen deprivation, knowing we could never reach the end.

This is what is so tantalizing about pi, that something so fundamental to the laws of geometry and mathematics should be ultimately inexpressible by numbers themselves, unobtainable by the human mind.  There is something, dare we say, Godlike in the number.  Pi is evidence of a higher mind at work in the universe, or not just at work, at play.  A cosmic humorist playing hide and seek with his creations, who has left a trail of breadcrumbs for us to follow, but which like the circle itself, like the Creator itself, is infinite.

1 comment:

  1. And even us doofus-type folks get to use π in our lame attempts at humor:
    Pi r square?
    No they ain't.
    Pi r round! (Hyuck, Hyuck!)

    It seems appropriate somehow that π is an infinite, non-repeating decimal. That means that...technically...we can never truly calculate the EXACT area (or circumference or diameter, etc.) of a circle. We can get so damn close as to make the difference virtually inconsequential...but we'll never be absolutely, spot-on perfect.

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