Pi’s Top Five


March 14th is not on the list of major holidays. This year, though, is particularly notable. Just one month after Valentine’s Day, the first five digits of Pi are embedded in the date 3 14 15 — that is a once in a century occurrence (only to be outdone in the year 1592, when the first 7 digits were embedded in the date). Considering the next three digits of Pi, 926, at 9:26 the first 8 digits will be embedded in date and time: 3 14 15 926.

It turns out this property is not completely unique to Pi — a large class of numbers can find their digits similarly embedded into a particular day. But Pi is a special irrational number that has driven historically important results. To celebrate Pi Day, I am offering a list of the most important mathematical results related to Pi (in reverse chronological order of their discovery).

5) Squaring the Circle

It turns out the vast majority of numbers are actually transcendental. This means that a number is not the solution of any one of those tricky polynomials equations (ax^n+bx^(n-1)+…+c=0 where the coefficients are rational numbers) that drive so many algebra students nuts. The question of Pi’s transcendence is tied to one of the great problems from antiquity, called “squaring the circle.” By proving Pi is transcendental, Lindemann conclusively demonstrated that it was impossible to construct a square with the same area as a given circle using only a ruler and compass a finite number of times. At minimum for a number to be transcendental, it has to also be irrational, which means its decimal expansion never ends or repeats. Pi unlocked this truth.

4) The Normal Distribution and Area under e^-(x^2)

The normal distribution plays an essential role in statistics, science, and finance because of —> Read More