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Thursday, May 22, 2008

PI AREN'T SQUARED

I suspect the problem begins with the oft quoted but not well understood phrase, “pie are squared.” In the first place, it’s not. In fact, you cannot square a circle. And, since, pi is the relationship between the length of the line forming a circle, divided by the distance across that same circle, and this somehow always works out to be 3.141592653589793238…etcetera, etcetera, ad infinitas, infeliciter, and never repeating,...
...to find the area of a circle you simply multiply pi times the radius of the circle, times the radius of the circle, or, in math-speak, A= piR squared. That means you can never turn a circle into a square of the exact same size: close but never exact. And it oesn’t matter if it is a great big circle or an itty-bitty one. Pi is always 3.141 etcetera, etcetera.If you are a math freak this is obvious, while the rest of us have to be satisfied with accepting that Pi is an irrational number: live with it. But I ask you, what is the value of knowing pi? I had a fourth grade teacher who was so obsessed with having her students memorize the value of Pi to twenty decimal places that she had us memorize the following poem: “Sir, I send a rhyme excelling, In sacred truth and rigid spelling, Numerical sprites elucidate, For me the lexicon’s full weight”. Each of the 20 words of that poem has the number of letters required to read out the first twenty digits of pi. I had to memorized that poem again in my thirties because as a ten year old I found most numbers irrational and I couldn’t spell the word Nantucket, let alone rhymes like “elucidate”. So this poem was as much a mystery to me then as the number Pi remains today.I am older now and I have made a fool of myself in front of an innumerable people, and have grown so used to making mistakes in public that I hardly notice the embarrassment anymore. So I admit I still find pi a puzzle. But every time I make a mistake, I learn something new, such as; never turn down a chance to use the bathroom, never loan money to attractive women, never invest in a Nigerian lottery ticket, never give out my social security number over the phone, and never question the value of pi.Legend has it that the great Greek mathematician Archimedes of Syracuse was struggling over the solution to pi when a Roman soldier blundered into his study. The old man supposedly snapped, “Don’t touch my circles!”, whereupon the chastised legionary pulled his Gladius and separated Archimedes’ head from his face. I suppose that if Archimedes had been sitting in his bathtub, as he allegedly was when he discovered that displaced water could be used to measure density (Eureka!), something else might have been separated. But, suffice it to say that before computers, finding pi was a great big pain in the Archimedes. He managed to figure out that pi was somewhere between 3 10/71 and 3 1/7. He might have done better if he had invented the decimal point, first.
About the year 480 CE the Chinese mathematician Zu Chongzhi figured out that pi was a little more than 3.1415926 and a little less than 3.1415927. After that the decimal point zealots took over. The German mathematician and fencing instructor Ludolf van Ceulen worked out pi to 35 decimal places, and in 1873 the amateur geek, William Shanks, worked it out to 707 decimal places. But William made one tiny little mistake in the 528th number and that threw everything else off. But it was such a good try that nobody noticed his screw up until 1944. Today computers have figured pi out to one trillion digits to the left of the decimal point and still no repeatable pattern has been detected. It is still a little bit less than 3.15 and a little bit more than 3.14. All that has changed is the definition of “a little bit”. It keeps getting smaller and smaller but it will never be zero.Still, pi remains the “admirable number” according to the devilish little Polish poetess Wislawa Szmborska. While being infinitly long it includes “…my phone number your shirt size, the year nineteen hundred and seventy-three sixth floor, number of inhabitants sixty-five cents, hip measurement two fingers a charade and a code, in which we find how blithe the trostle sings!” (…and no, I have no idea what or who the hell a trostle is. The Oxford English Dictionary doesn’t either. Do you?)I do know that a physician and crackpot amateur mathematician from Solitude, Indiana named Dr. Edwin J. Goodwin thought that he had “solved” pi to the last digit and none of this irrational numerical horse feathers for him! And he decided to make it his own personal private property. But in order to profit from his discovery (you know how wealthy the Pythagoras estate is) Dr. Goodwin needed a legal endorsement. And rather than subject his brainchild to the vagaries of the copyright peer review, the good doctor instead offered his theory as an accomplished fact to the local politicians. The proposal, Indiana House Bill 246, “…an act introducing a new mathematical truth and offered…to be used only by the State of Indiana free of cost…provided it is accepted and adopted by the official action of the Legislature…”, actually made it through the Committee on Canals and Swamps in record time, and was passed by the full house on February 5, 1897, by a vote of 67 to 0.
Unfortunately, in the Indiana Senate, some wiseacre showed the bill to a visiting Purdue party pooper, Professor of Mathematics C.A. Waldo. The lawmaker then asked if the professor would like the honor of meeting the amazing Dr. Goodwin, and Professor Waldo replied that he already knew all the lunatics he cared to know, thank you very much, and with that comment Dr. Goodwin’s brief bubble of fame was burst. On February 12, 1897 any further vote on the bill was postponed indefinitely. It was not a victory for logic so much as an avoidance of a victory for ignorance, which is pretty much the same thing that happened in Tennessee about 30 years later.Still pi remains one of the most popular mathematical equations, if mostly poorly appreciated by those of us who aren’t trying to generate a random number or navigate a jet plane across the North Pole, or predict the next stock market bubble, or launch a satellite, run a radio station, process an X-ray or a Cat-scan, drive a submarine, drill for oil, purify gold or etcetera, etcetera, ad infinitas, infeliciter.
Just trust me, and always trust pi. It lifts your spirit, gives you a sense of security and keeps your circles on the square. To share it just try singing..."Pi, Pi, Me oh my, Nothing tastes sweet, wet, salty and dry, all at once, ...oh my, I love pi!

- 30 -









The Pi pie, provided with the generous kind grace of "VROG in Bristol" http://www.flickr.com/photos/vrog/1441303189/

1 comment:

  1. That pie image is great.
    But it's protected by copyright.
    I know.
    Because I baked that pie.
    And took the photo.

    The original is on my flickr pages here:
    http://www.flickr.com/photos/vrog/1441303189/

    I'd be happy for you to keep the image on your blog - but only if you can credit "VROG in Bristol" and link to the original on flickr.

    Thanks
    Rob

    ReplyDelete

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