Friday, May 7, 2010

Is ' pi ' Really THAT Mysterious?

Thousands of words have been written about the history and study of the mathematical constant called ' pi '.  Some might be confused that we can call pi a 'constant' when we don't even know part of what pi is.

Okay, I stand corrected here, although it isn't really pertinent. It seems there IS a formula out there whereby given a value N of the nth position to the right of the decimal on PI, the next number can be determined.

In a sense, to some nerd-ish technical degree, pi is only an estimation. {perhaps it would be better to say that PI need only be as accurate as the problem requires}
Of course, pi has always been an estimation (rounded).  Throughout history pi has been estimated to be everything from 2, to 4.  When they started building big things like the pyramids, the ancients either had a close approximation which worked, such as 3, or they used actual ratios which closely approximate pi and fractions of pi.

[For some insight into the significance of the mathematics of the pyramids, check out this old classic by Charles Piazzi Smyth:

New Measures of the Great Pyramid (1884) courtesy of Archive.org - a site I highly recommend ]

Pi is fascinating as a number by itself.  Many have looked for patterns in the non repeating decimal or solved it to thousands of places hoping to see a repetition or a finite end.  Of course it goes on forever.

But these fascinating features of pi, are easily explained.  Perhaps so easy that it is overlooked.  The fact is that pi is what makes a circle ROUND.  it is a constant - present equally in every circle, but it is an endless, un-resolvable constant.

But isn't that true of the circle itself?  Would we expect to find something finite in a circle that is REALLY a line which continues forever?  If pi were a finite number, then a circle wouldn't be round, it would be made up of a bunch of short flat lines, which, if you zoomed in close enough, you could see on every circle.  But they aren't.

{Again, I will accept a clarifying point here. All irrational numbers are finite in the sense of where they stand on the real number line. PI is greater than 3 and less than 4 or greater than 3.140 and less than 3.142. So, technically, finite. But in the sense of its exactness, its fractional portion is infinite and unknowable as a whole just as the set of real numbers is unknowable because it is infinite, even if there is a predictable pattern to the set of real numbers.

So next time you are pondering the mysteries and simple beauty of the earth, remember that pi isn't an enigma, it is merely the number that makes a circle curved.


Reverend Mike
Copyright 2010
MEB BEB



Stonehenge - National Geographic photograph