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Notes on Pi

Pi, which is denoted by the Greek letter, is the most famous ratio in mathematics, and is one of the most ancient numbers known to humanity. Pi is approximately 3.14 - the number of times that a circle's diameter will fit around the circle. Pi goes on forever, and can't be calculated to perfect precision:

3.1415926535897932384626433832795028841971693993751....

This is known as the decimal expansion of pi. No apparent pattern emerges in the succession of digits - a predestined yet unfathomable code. They do not repeat periodically, seemingly to pop up by blind chance, lacking any perceivable order, rule, reason, or design - "random" integers, ad infinitum.

In 1991, the Chudnovsky brothers in New York, using their computer, "m zero", calculated pi to two billion two hundred and sixty million three hundred and twenty-one thousand three hundred and sixty-three digits (2, 260, 321, 363). They halted the program that summer.

Pi has had various names through the ages, and all of them are either words or abstract symbols, since pi is a number that can't be shown completely and exactly in any finite form of representation. Pi is a transcendental number. A transcendental number is a number but can't be expressed in any finite series of either arithmetical or algebraic operations. Pi slips away from all rational methods to locate it. It is indescribable and can't be found. Ferdinand Lindemann, a German mathematician, proved the transcendence of pi in 1882.

Pi possibly first entered human consciousness in Egypt. The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 BC by a scribe named Ahmes. He began scroll with the words: "The Entrance Into the Knowledge of All Existing Things" and remarks in passing that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which is composed of various mathematical problems and their solutions, the area of a circle is found using a rough sort of pi.

Around 200 BC, Archimedes of Syracuse found that pi is somewhere about 3.14 (in fractions, Greeks did not have decimals). Knowledge of pi then bogged down until the 17th century. Pi was then called the Ludolphian number, after Ludolph van Ceulen, a German mathematician. The first person to use the Greek letter "¼" for the number was William Jones, an English mathematician, who coined it in 1706.

Physicists have noted the ubiquity of pi in nature. Pi is obvious in the disks of the moon and the sun. The double helix of DNA revolves around pi. Pi hides in the rainbow, and sits in the pupil of the eye, and when a raindrop falls into water pi emerges in the spreading rings. Pi can be found in waves and ripples and spectra of all kinds, and therefore pi occurs in colours and music. Pi has lately turned up in superstrings.

Pi occurs naturally in tables of death, in what is known as a Gaussian distribution of deaths in a population; that is, when a person dies, the event "feels" pi. It is one of the great mysteries why nature seems to know mathematics.

NOTE: The above information was gleaned from an article in "The New Yorker", March 2, 1992, called "Profiles: The Mountains of Pi"



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