Thursday, March 14, 2013

Happy Pi Day 2013

That we celebrate Pi Day is curious. Granted, e = 2.71828… does not lend itself well to February 71 or the 27th day of the 18th month, whereas March 14 exists and finds millions of kids in school mathematics classes.  Yet our fascination with Pi – versus the speed of light, Planck’s Constant, G, or anything else – may speak to a basic belief that reality is not just easy to understand: it is fun. 

You can make a pretty good compass from a length of string and a thumbtack. In ancient Egypt, geometers were called “arpedonapti”, those who knot ropes.  (Garden of Archimedes at the University of Firenze (Florence) Italy in English here.)  You can make a right angle by knotting any convenient length of string into a 3-4-5 triangle. With a known right angle, much else can be drawn and thereby computed.  This was important to the Egyptians because the annual flooding of the Nile erased boundary lines.  

The compass is more reliable, precise, and accurate than a knotted rope. The inventor that instrument has been lost to time.  We can call him "Daedalus" for convenience.  Clearly, the architect’s compass (bow compass or divider) had to have been a specific and sophisticated invention. The earliest known is from the 6th century BCE.  Wikipedia on the Drafting Compass.  Wikipedia on the Divider Caliper.  The invention of formal geometry is credited to Thales of Miletus. Pythagoras of Samos was a near contemporary. This was also the time when philosophy was supplanting religion for explanations, when coinage was replacing commodities as stores of value, and when hereditary rulers were replaced first by tyrants and then oligarchies and democracies. Those were heady times

By the European Middle Ages, the importance of builders (masons) made the compass a symbol for God’s work and order within the universe. 
William Blake's Ancient of Days
from Wikimedia commons

The opinion that a benevolent God placed us within His creation was different from the classical view that life is unpredictable because even the gods cannot change the work of the Fates, three blind sisters who spin, measure, and cut the threads of our lives.  In our postmodernist era, we have fallen back to that pagan view, perhaps best stated by Albert Einstein.  While he denied that God plays dice, he felt that the universe is stranger than we can imagine.  That may well be true – and it may also explain some aspect of our fixation on pi.  It is at once understandable and unpredictable. 

Yet, paradoxically, formulas to generate pi are known.  (See the presentation on “Machin’s Formula” by Dr. Milan Milanović here.)  Interestingly, you can find the nth digit of pi without knowing the preceding numbers.  (See "Fun Facts" from the mathematics department of Harvey Mudd College here. )

One Million Digits of Pi:
Four Million Digits of Pi:

Previously on Necessary Facts:

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