Today, as you probably know, is the pi-est of pi days in American: 3.14.16, or pi rounded to four decimal points. I say in America because much of the world writes dates as day-month-year instead of month-day-year, so for them it’s 14.3.16 – not too exciting. (Bonus material: Terrific math blogger Vi Hart hates pi day – here’s her latest video rant about it.)
In a math-phobic world, pi is unique as a cultural icon born from mathematics. It stands for math in casual conversation in the way that “Einstein” stands for science, “Picasso” for painting and “Beethoven” for western classical music.
But why? Specifically, why do we get psyched about pi (3.14159…) and not about the similar constant known as e (2.71828…)?
Those two are among the five important numbers to mathematicians, along with 0, 1 and i (square root of -1).
Pi shows up in formulas related to cycles and rhythm, as Mathematician Steven Strogatz explained in the New Yorker last year, while e shows up whenever you’re analyzing any type of growth. Both describe the innermost workings of reality.
Both pi and e are irrational and transcendental, meaning neither is the root of a polynomial equation with rational coefficients (which is important, although like many deep mathematical truths it’s hard for laymen to understand exactly why). Both of them show up all over the place in seemingly unrelated places – for pi, most weirdly as the limit of how much river twist and turn.
They even share a person: Leonhard Euler, who’s in the running for the title Greatest Mathematician Of All Time, popularized the use of the Greek letter pi for the ratio, and did so much early work with e that it’s named after him, as Euler’s constant. Euler’s identity 0 = (e^(i*pi)) – 1 is often called the most beautiful creation in mathematics because it relates all five of them in an unexpected way.
So there’s not much to choose mathematically. The reason we get psyched about pi is history and accessibility .
Pi was the first irrational number to be studied – although the square root of 2, in the form of the length of the diagonal of a unit square, was probably the first irrational discovered. Humanity has pondered pi for millenia.
On the other hand, e only was discovered* in the 1600s with the development of logarithms.
As for accessibilty, we all understand at least somewhat what is meant by the ratio of diameter to circumference of a circle, but who knows what the natural logarithm is? There’s no way something as relatively esoteric as e would ever become part of pop culture.
Of course,what really seals the deal is the pi = pie homonym thing. If Euler had used lambda instead, you wouldn’t be hearing any of this.
* or invented, if you’re so inclined.