Happy Pi Day!
March 14, 3.14, the common rounding of the number pi, is the day for our inner math nerd to shine, or a day for us to pull out and pet our math phobias.
Pi is the ratio between the diameter of a circle and its circumference; C/d = 3.1415926… (the dot dot dot represents that pi has an unlimited succession of nonrepeating decimal digits.) Though irrelevant to reaching an accurate answer to a problem, pi has been calculated to over 10 trillion places – a number that is as amazing as the one representing the U.S. national debt.
The pi ratio is also used in a variety of formulae to determine area and volume of circular and elliptical objects, the motions of pendulums (watch the pattern they inscribe in sand), and for electrical circuits.
Contemplating pi drove ancient mathematicians crazy. The idea that a relationship between the diameter of a circle and its circumference was not rational, i.e. could not be represented as a fraction, like ½, was not, well, rational. Mathematicians gave a name to these kind of numbers: they call them irrational.
The Babylonians first expressed the relationships in a circle about 4000 years ago as 25/8. In 1650 B.C.E., Egyptian mathematicians calculated the ratio as 256/81. And then in 250 B.C.E, the Greek mathematical genius, Archimedes, determined that the ratio was somewhere between 223/71 and 22/7 by using polygons to "square the circle."
In 150 B.C.E., Ptolemy, using Archimedes polynomial method of squaring the circle, fixed the value of pi at 3.1416; close enough for most of us.
The idea of irrationality drew mathematicians like honey, and they continued to calculate their pi-accuracy. In the 17th century, mathematicians had advanced the calculations to 39 places, which is all we need to make accurate measurements, including the volume of our universe. They used a new technique, infinite series, to extend the accuracy. It is one of the techniques we are supposed to learn when we take calculus.
In 1706, the Welsh mathematician William Jones, who was a close friend of Isaac Newton and Edmund Halley, proposed the Greek symbol p, pronounced 'pie', to represent the ratio, a good idea that was quickly adopted.
Though it is irrational, pi represents one of the constants of nature. It is an unvarying relationship, grounded in reality, which allows us to understand the world, and universe, around us.
Pi is also a transcendental number, a concept that transcends my ability to understand, but has something to do with it not being algebraic.
The simple beauty of pi inspired Congress to pass a resolution in 2009 to declare March 14 "Pi Day." March 14 has the added bonus of being the birthday of Albert Einstein, who was born in 1879.
Who can resist a transcendent, irrational number that is a constant?
So, enjoy a bit of pi(e) today to celebrate!
Reach Frank Daniels III at email@example.com, 615-881-7039 and on Twitter @fdanielsiii.