Let’s visit the number land once again — this time for none other than Pi. It is a celebrity number, defined as the ratio of simplest shape, circle, to its diameter. Tech giants compete to calculate the maximum number of digits of Pi. There are competitions of Pi digit memorization. Isn’t it insane that the world record for Pi digits memorization is 100,000? As beautiful as it may sound, uglier it is, the infinite and non-repeating property of Pi, simply leads to mess and madness and chaos. But being transcendental and irrational, isn’t it boring. There are various numbers like this.
So, what makes Pi so iconic? Pi is omnipotent. It existed even prior to The Big Bang. The meandering ratio of the river to the orbits of satellites. It’s not just about circles, Pi helps us understand curves, periodic and oscillating systems. It is used in electromagnetics and music as well. In statistics, it is used to measure the area under the bell curve.
Despite all its applications, Pi is so devoid of patterns that it passes every randomness test with flying colors. It is not only random, but that any string of them occurs just as much as any other of the same length. This means if we encode Pi in base 26, representing each number as alphabets then we can find all of the work of Shakespeare. It would be merely absurd to question at which decimal position. Doesn’t it amuse you, that such an elementary formula gives rise to such a plethora of information? Moreover, Pi opens up the window for transcendental numbers. Most of the numbers on the number line are transcendental, and we have rarely visited that road. This implies how limited human knowledge is.
But how do we calculate Pi? We can’t tell the exact value of Pi but only approximate. The first recorded algorithm to rigorously calculate Pi was Polygon Approximation. Mathematicians inscribed and circumscribed the polygon around a unit circle and thereby calculated the perimeter of both the hugging polygons to find the lower and upper bound of the Pi. Later, this was revolutionized by converging infinite sums. Now in the age of technology, we can calculate the value of Pi with an accuracy within 0.04% through iterative algorithms. What if we calculate the exact value of Pi? Will it be a breakthrough or will it be just another day, who knows? Until then enjoy the chaos of Pi.