"Pi" (the ratio of the length of the circumference of a circle to its diameter) is one of the most elusive concepts in the history of mathematics. The process of trying to understand this number goes from near the beginning of recorded civilization to the present and may very well never end, for as far as we can ascertain, neither does pi.
Pi is an irrational number, which means that it cannot be expressed as the ratio of two integers. Its decimal expression begins "3.14159..." however its terminus has never been found – and in all possibility may not exist – nor has any repeating sequence within the decimal chain.
The Greek Symbol for Pi
In 1706 William Jones introduced the use of the lower-case Greek letter "π" in his Synopsis Palmariorum Matheseos as shorthand for the value, borrowing it from the first letter of the Greek word "perimeter".
π is first recorded as being used by mathematicians in the ancient city of Babylon at around 2000 BC (they figured π at 3 1/8) and then in Egypt, as evidenced by the Rhind Papyrus (circa 1650 BC), whose mathematicians came up with π = 3.16049.
Archimedes Calculates Pi
In the Third Century BC, the Greek scholar Archimedes created a method for calculating π that was the most accurate yet. He proved that it lay somewhere in between 223/71 and 220/70 by using a method of describing the circumference and diameters of polygons placed inside and outside a given circle. When more and more sides were added to each polygon, they began to more closely equal the circle in shape and area whose circumference was trapped between them, the inner polygon growing progressively larger, the outer polygon smaller.
Fibonacci, Newton, van Ceulen Extend the Decimals
The development of the accuracy of the π formula (or more appropriately, our understanding of it) continues on through history. In 1220 the mathematician Leonardo da Pisa (also known as Fibonacci) found π = 3.14188; in 1665-66, Sir Isaac Newton extended the calculation to 16 decimal places. Ludolph van Ceulen was the last to use Archimedes' method to extend π's accuracy to 35 places, a calculation (known thereafter as the "Ludolphine Number") which was later inscribed on his tombstone.
In 1874 William Shanks published his calculation of π all the way to 707 decimal places only to have his work proven flawed 71 years later in 1945 when D.F. Ferguson found Shanks's calculation incorrect from place 527 onward.
Pi's Decimal Calculation Reaches the Billions
In 1997 a Hitachi SR2201 computed in a little over 29 hours, π to 51.5 billion digits, yet there is no evidence that we are substantially closer to reaching the end of the number than Newton was with 16. The decimal places simply continue without ever repeating a sequence, each number representing a value ten times more exact than the previous one, and the ultimate, exact value of π (assuming it even exists, considering the concept of numerical infinity) remains a mystery.
Sources consulted:
Asimov, Isaac. Asimov's Biographical Encyclopedia of Science and Technology, Revised Edition. Garden City, New York: Doubleday & Company, Inc., 1972
Blatner, David. The Joy of Pi. New York: Walker & Company, 1997.
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