First of all, why Pi?
The mathematical symbol for Pi “π” is a Greek letter, derived from the first letter of the Greek words “περιφέρεια”, meaning periphery, and “περίμετρος”, meaning perimeter.
The earliest known use of the symbol was by Welsh mathematician William Outright in 1647, but it only became popularised in 1748 by Leonhard Euler in his book Introduction to Analysis of the Infinite.
Mathematically, Pi is used to calculate the volume of a sphere or the circumference or area of a circle.
So, why all the fascination and curiosity with Pi?
First, we have to trace the history of Pi and then we will discuss the discoveries of the decimal places of Pi. We will see that Pi is both an irrational number, a transcendent number, and perhaps a normal number. We will then finish off with some mysteries surrounding Pi.
Even if you do not like mathematics, algebra, trigonometry, Gauss, Thales, Pythagoras and these kinds of theorems, I assure you that you will find your niche somewhere in this article!
To become a real expert on Pi in maths class and know everything there is to know about mathematics, all you really have to do is read!
If today, the most powerful computers are able to determine up to 13 trillion decimal places of Pi, you can imagine that this has not always been the case.
Archimedes’ method was used for 2000 years after his death. Not bad, eh?
The perimeter of the circle (blue) is between the perimeter of the green hexagon and that of the purple hexagon according to Archimedes’ method. (Source: math.psu.edu)
Do you know any of the most famous mathematical paradoxes?
Having proved his method, many mathematicians will use Archimedes’ method to determine more and more digits of Pi.
Who will find the most decimal places of Pi? Source: visualhunt
The West didn’t start the race to estimate Pi until another few centuries later, although as early as the 17th century Leonardo da Pisa Fibonacci proposed interesting approximations of Pi.
The real turning point in the calculation of Pi was the discovery of analysis and differential calculus. Many mathematicians like John Wallis, Leibniz, James Stirling and Newton understood that Pi was not only geometrically apprehensible, but could be in the form of a series.
Man has found other ways to have fun with maths and Pi: recite as many decimal places as possible!
There’s even a group of individuals who can list off the first 1000 decimals of Pi (the 1000-club).
Notable achievements include Daniel Tammet who in 2004 cited 22,514 Pi decimal places in just over 5 hours.
The current record is held by a Japanese native who recited 100,000 decimals of Pi.
If you want to get started, it will only take you sixteen and a half hours …!
If Pi is indefinite, and therefore mysterious, do you know any of the greatest mysteries in mathematics?
Let us now return to the crux of these two little letters, which still reveal many surprises!
Pi is an irrational number, which means it cannot be written as a fraction of two whole numbers (like a rational number).
In fact, its decimal places are neither periodic nor finite. In other words, the decimals of Pi are not predictable and no model could predict them.
The first mathematicians discovered the principles of the indeterminable and abstract infinity, they even saw Pi as an insult to the omniscience of God!
Pi is a transcendental number, which means it cannot be the solution to any polynomial equation with integer coefficients.
However, formulas bind Pi to other mathematical constants such as the Golden Ratio, which corresponds exactly to the construction methods of the Fibonacci sequence.
The fact that researchers still do not know if Pi is a normal number (a number with a finite sequence of decimal places) has had a massive influence on our sustained interest with Pi.
In almost four millennia, this number has still not revealed all its secrets!
Oh yes! Pi is all around you!
The omnipresence of Pi, outside of geometry class, is really intriguing to many researchers and math enthusiasts.
Oh yes! Pi is all around you! Source: visualhunt
Pi is effectively the limit of certain continuous fractions, a nested radical.
Research carried out on transcendental and irrational numbers, largely related to Pi, provide an answer to the squaring of the circle. It is in fact impossible to construct a square with an area equal to that of a given circle.
In statistics and probability, the number Pi also appears, like in Buffon’s needle problem. Learn about other maths problems.
More interestingly, the ubiquity of Pi goes beyond the boundaries of simple mathematics.
Pi exists wherever a circle is exists, for example in a bulb, the sun, an eye and DNA!
Pi is even present in the equation of Heisenberg’s famous uncertainty principle, which seeks to elude our understanding of the universe.
What’s the link between Pi and an Egyptian pyramid? Source: visualhunt
What’s the link between Pi and an Egyptian pyramid?
Pi also appears in mythical constructions, which have no apparent connection to circles.
This is particularly the case for the famous pyramid of Cheops.
Numerous works show that Pi is the ratio between the perimeter of the base and double the height of the pyramids. This mathematical ratio for Cheops is almost equal to Pi (I’ll let you calculate the perimeter!).
Was this the architect’s intention or is it a pure coincidence?
Finally, for those who categorically dissociate mathematics from literature, Pi reconciles the two subjects. Poems allow us to learn the first few decimal places of Pi (127 in the full poem), so why not wow your friends! The idea is that the number of letters in each word corresponds to a decimal point of Pi.
This brief stanza gives thirteen digits of π:
See, I have a rhyme assisting
3 1 4 1 5 9
my feeble brain,
2 6 5
its tasks sometimes resisting.
3 5 9 9
Why not learn the whole poem!
You have been won over by Pi! Make sure to raise a glass to one of the greatest mathematical discoveries on the next “Pi day”, every 14th of March.
To finish on an even funnier note, did you know that 2 scientists actually used maths to figure out the lead character in GOT? Tell that to your maths teacher!