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: http://www.piday.org/million/
Four Million Digits of Pi: http://zenwerx.com/projects/pi-digits/pi/
Previously on Necessary
Facts:
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.