Happy ~3.14159… Day!

Today is Pi Approximation Day. This day celebrates the fractional representation of π, which is 22/7 = 3.14285….

The date originates from day and month nomenclature, rather than month and day nomenclature.

Let’s look closer at π:

When we measure the distance around a circle (starting and stopping at the same point) compared to the distance measured across the circle’s center, we are computing a ratio (and calculating a number). As curious as this intuitive measurement seems — a simple ratio of girth versus breadth — the resulting number is the mathematical constant π, defined as π = C/d. Here C represents the circumference of the circle, and d is the diameter of the circle. We learn that the distance around any given circle is a little more than three times the distance across it.

Pi itself is an irrational number. Irrational numbers are numbers that have no terminating digit after its decimal point, including no terminal repeating digits or terminal sequence of digits. Nevertheless, only the first 39 digits of π are needed to accurately calculate the spherical volume of our entire universe. Thankfully, however, when thinking about π or invoking its use during hand calculations, most people (including many math students) are safe using the first 5 decimal places, such that π = 3.14159.

Pi is used in the following non-exhaustive list of formulas:

  • Circumference, C, of a circle: C = 2πr
  • Area, A, of a circle: A = πr2
  • Volume, V, of a cylinder: V = πr2h
  • Volume, V, of a sphere: V = (4/3)πr3

For each of the aforementioned equations r is radius, and pertaining specifically to the volume of a cylinder, h is height.

Celebrate Pi Approximation Day!