Pi

If you were to measure the diameter of circles of many different sizes, you would notice that the ratio between the circle's circumference and its diameter remains constant no matter what its diameter is. This ratio is represented by π (that's the Greek letter pi).

The earliest-known record of this ratio was written by the Egyptian scribe Ahmes around 1650 B.C. and has been preserved in the Rhind Papyrus. In one passage, Ahmes implies that this ratio is (¹⁶/₉) ², or 3.16049... . To five decimal places, the actual value of π is 3.14159. Ahmes' value was within one percent of π's true value.

What kind of a number is π, though? It turns out that π is not rational; that is, it cannot be written as the ratio between two numbers. Furthermore, π is transcendental; that is, π cannot satisfy any algebraic equation. Since this number is irrational and transcendental, the digits of the number are inherently unpredictable.

Currently, over 51 billion digits of π have been calculated. You might be wondering: why? Certainly nowhere near that many digits are required in calculations to provide results that are very close to the "exact" value. There are several reasons. One reason is that calculating π to so many digits shows how powerful a supercomputer is. Another reason is that mathematicians are interested in whether the sequence of numbers in the decimal representation of π is as random as it looks. It is possible that we may discover some sort of pattern within the decimal places of π if we have enough data.

View a chronology of calculating pi.

One recently-published book about pi that I enjoyed was called The Joy of π by David Blatner (for more information on this book see my bibliography page).