π=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

Since today is March 14th (3-14), I thought I would take this as an opportunity to learn a bit more about the number π, which is a mathematical constant for the ratio of a circles’ circumference to its diameter (π = C/d), and share what I found.

How this Greek letter came to be used to represent this particular ratio is a bit clouded. As early as 1647, William Oughtred used it to represent ratios of periphery and diameter. π ma have been chosen because it is the first letter in the Greek spelling of periphery. But it was not until 1706 that William Jones first officially used π to mean the ratio of circumference to diameter in his “A New Introduction to the Mathematics,” but in this work he credits many of his equations, possibly including π, to John Machin. Where Machin got, I have no idea. Even after 1706, π was not adopted by the mathematics community until Leonhard Euler started using it in 1736. Euler frequently corresponded with other mathematicians across Europe, and as a result of this, the use of π spread and became universally adopted.

However the symbol came to be used, the concept of π is very old indeed. The oldest written approximations of π come from Egypt and Babylon where each culture estimated the value of π to within 1%. In Babylon, a clay tablet was found that dated to 1900-1600 BCE on which was writing on geometry that included a value for π as 25/8 ~ 3.1250. In Egypt, the Rhind Papyrus, which was written around 1650 BCE but which was a copied from an older document dated around 1850 BCE, includes a formula for the area of a circle which includes a value for π as (16/9)^{2} ~3.1605. Further, the Great Pyramid at Giza has a basal perimeter of 1760 cubits and a height of 280 cubits. This ratio, (1760/280) ~ 6.2857 which is 2π. Some people believe that this is proof that the architects of the Great Pyramid knew about π and were trying to incorporate the proportions of a perfect circle in the pyramid.

Some of the properties that make π such an interesting ratio include that it is one of the irrational numbers. This means that it cannot be represented as the exact ratio of two integers. For example 6/2 = 3. Instead, π must be represented as a complex fraction, which is one that never resolves, but instead goes on for infinity getting ever more accurate, but never exact. This infinite, non-repeating property of π is another reason it is interesting. The numbers in π seem to be truly random. This makes π a sort of natural random number generator which makes it useful in statistics and also in internet security. The value of π is used in astrophysics where π, to 39 decimal points, has been shown to calculate the volume of the universe to within one atom! Yet another use of π is in Heisenberg’s Uncertainty Principal. This principal states that it is not possible to know both the change an atoms position and the change in that atoms momentum simultaneously to an infinite degree of precision. Heisenberg’s Uncertainty Principal is usually stated as: Δχ Δp ≥ h/4π

So go out, enjoy a slice of pie, think about some math, and have a great Pi Day!

Read Full Post »