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Pi
Pi, or the Greek letter ( ), is used in mathematics as the symbol for the ratio of the circumference of a
circle to its diameter. This ratio is a universal constant, meaning that it is always the same for any size
circle. Several financial models, as well as many other mathematical and physical equations, contain .
The most notable being the equation to find the area under the Normal distribution. Finding the area of
a circle (A = r2, where r is the circle’s radius) or the volume of a sphere (V =4/3 r3), for instance, both
require knowledge of the value of
The approximate value of to twenty decimal places is 3.14159265358979323846…The ratio is actually
an irrational number, meaning that its decimal places go on infinitely without repeating or ending in
zeros. Mathematicians have found many unending equations with solutions equal to ; one of the
simplest is = 4(1 – 1/3 +1/5 -1/7 +1/9 …). Computers can use such equations to quickly estimate with
great accuracy; in this way the value of has been figured to more than 1.2 trillion (1,200,000,000,000)
decimal places.
The ratio was known in ancient times, and various approximations of its numerical value were used. In
the Bible, the value of was taken to be 3. The Greek mathematician Archimedes correctly asserted that
the value was between 3 10/70 and 3 10/71. There is a not-uncommon parlor trick that entails the
challenge of memorizing to as many places as possible.