March fourteenth: 3/14 or 3/14 if we read it in English nomenclature. When saying “three fourteen” a number quickly appears in our minds that reminds us of school.
It is also very possible that when we hear it we follow the sequence: fifteen, ninety-two, sixty-five… as far as we can remember the figures of the singular number Pi (π).
The US Congress in 2009 officially declared that this day, March 14, would be the π day.
It was enormously successful from its inception, and the idea grew until in 2019, UNESCO declared it the International Mathematics Day.
Since then, every year more and more people have joined the celebration, with π as a symbol of those of us who love mathematics.
Pi is not really a number
Let’s start by clarifying something, Pi is the sixteenth letter of the Greek alphabet (π) and in mathematics we use it to represent something much more interesting than a number (which I am not saying that numbers are not). So, the first oddity of Pi is that, which is not a number. But then, if it’s not a number, what is Pi?
Pi represents the proportion of the length of the circumference to its diameter. A proportion that has the particularity (here its second rarity) to be constant, that is, the same value is always valid no matter how big or how small the circumference is.
In particular, in Euclidean geometry – which we owe to Euclid (325-265 BCE) and which assures us things such as that a single straight line passes through two points – the constant value of Pi is as special (and there are already three of them) as to be irrational.
It is not that he has lost his mind but that, despite being the result of dividing the perimeter by the diameter, It can never be expressed as the division of two integers..
If the diameter of a wheel is an “exact” value, without decimals, the space it will cover when making a turn will not be. But then how much will it be? We are approaching a key question, the value of Pi…but first let me continue with another of his oddities, the fourth now.
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Pi is transcendent. It is not that it is so important that it transcends (that too) but that it is transcendent, without n. This mathematical property assures us that Pi will never be the solution of any polynomial.
Polynomial? Surely you remember him from his mathematics studies. Polynomials are equations in which the unknown appears raised to one or more natural numbers, for example x2 + x + 3 = 0.
Well, no matter what exponents and numbers are used, there is no polynomial for which x is worth Pi. It is also worth mentioning that this is a property that many numbers do not meet so, at this point, it has already been proven that Pi is rare but the best is still missing. Now yes, let’s talk of its value.
The elusive value of Pi
As we said at the beginning, the constant value of Pi (in Euclidean geometry) is 3.141592… but, precisely because it is irrational, we know that it will have infinite decimals. Infinite, as it sounds, without end and, to make matters worse, in this case it is not only that they are infinite but that They don’t follow any pattern..
They appear to be placed at random, with all figures from 0 to 9 having the same probability of appearing. In fact, their values can be used as a random number generator and it is possible to search among them for any sequence of figures, even the ID number of any person, who is sure to be found somewhere.
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However, the most important thing about this property of Pi is that it has become a source of inspiration for the work of many people.
Since ancient times (there are indications that the Babylonians already knew about Pi in 2,000 BCE) efforts have been made to establish its value with the greatest possible precision. In particular, one of the first to bear fruit was that of Archimedes of Syracuse (287 – 212 BC), who designed a method to limit the value of this rare constant.
Archimedes used polygons that were inscribed (those that are located within the circle) and circumscribed (those that contain the circle inside). In this way, the value of the perimeter of the circle would always be between the perimeter of the inscribed polygon and that of the circumscribed polygon.
By adding more and more sides to the polygons, Archimedes managed to give an interval of values for Pi, which had a maximum error of 0.040% on the real value… come on, close, close.
Archimedes’ idea was followed by many others of a very diverse nature, some even from the point of view of probability and statistics, as was the case of Georges-Luis Leclerc (1707-1788), the Count of Buffon.
In particular, Leclerc encountered the number Pi while trying to determine how likely it was that a needle thrown across a set of parallel lines would fall across one of the lines. After various calculations he came to the conclusion that, if the lines were separated by the same distance as the length of the needle, This probability was 2 divided by Pi.
In this way it was easy to approximate Pi by throwing many needles, observing the proportion of these that actually cut the parallel lines and comparing it with the exact probability.
However, with the arrival of the computing age, the fifth Pi oddity appeared, be a computable number. In particular, Alan Turing, back in 1936, defined that a number is computable if there is an algorithm that allows us to approximate its value with a predetermined number of decimal places.
63 billion decimal places of Pi have been calculated
Following this premise, in 1949 an ENIAC machine managed to break the record established to date by humans and calculate the first 2037 decimals of Pi, giving the starting signal for a race that has reached 63 billion (European) from figures with which it was calculated in 2021 by a team from the University of Applied Sciences of the Swiss canton of Graubünden.
But Pi is not just a curious mathematical entity that has plucked the strings of human thought since ancient times. Pi is, as Rhett Alain assures, an astonishing number that appears naturally where we least expect it: in the estimation of our position by GPS, in the movement of the pendulum of a wall clock or even in the way in which an assistant By voice it is capable of recognizing that the user wants, for example, to tell a joke.
But, above all, Pi is the perfect excuse for us to celebrate mathematics and everything it gives us every March 14th. Happy International Mathematics Day!
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