In Mathematics, the constant ‘Pi’, or π, is an irrational number with digits after the decimal point stretching to infinity. Every number can be found within Pi. The constant is so fascinating that March 14 is celebrated as “Pi Day” and there are competitions to recite the digits. But how was it discovered and where in Maths is it used?
In Mathematics, the constant ‘Pi’, or π, is an irrational number with digits after the decimal point stretching to infinity. Every number can be found within Pi. The constant is so fascinating that March 14 is celebrated as “Pi Day” and there are competitions to recite the digits. But how was it discovered and where in Maths is it used?
Did you know that the symbol “π” – or, “Pi” – does not equal 3.14 or 22/7? It is in fact an irrational number which has an infinite number of digits which never end.
The number “π” is the most recognizable mathematical constant in the world. It is because of the numerous uses it has in the field of geometry, astronomy, and many others. Every human being who is a student is introduced to π early, when they learn about circumference and area of a circle. Later, they learn that surface areas and volumes of various solid figures like spheres and cylinders also make use of π. How was this constant discovered?
The discovery of π is attributed to the Babylonians who lived in around 2000 BC. It was observed that the ratio between circumference of a circle and its diameter was constant for a circle of any size. Today, we know the circumference is 2πr and diameter is 2r and so, their ratio is π itself. But back then the value of this constant was not known. Many mathematicians asked themselves the question- How to calculate pi? So this led to several attempts by various people through many centuries to calculate the exact value of this ratio. As measuring the circumference precisely was not an easy task at the time, different methods have been used to do it.
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The method the Babylonians used was to increase the number of sides of a regular polygon to a number as large as possible so that the regular polygon can be approximated to be a circle. The illustration below, where “n” represents the number of sides, shows this.
The greater the number of sides in a polygon, the closer is the value of the circumference of the polygon to the circumference of the circle. The first person to calculate the value of π to a figure very close to the actual value was the famous Greek mathematician, Archimedes, who also discovered buoyancy force. He used a polygon with 96 sides! Later on, a Chinese mathematician used 3,000 sides.
Earlier, there was no symbol to denote the number Pi. According to a History Today article, mathematicians and scientists used to refer to it as “the quantity which, when the diameter is multiplied by it, yields the circumference”. But this was not very practical due to several uses of Pi. So, the symbol ‘π’ was introduced by the mathematician William Jones, a friend of Sir Isaac Newton, in 1706.
As mentioned earlier, π is an irrational number. Irrational numbers are the ones that cannot be written as a ratio of two integers. Such numbers have a unique property: when written in decimal form, these numbers never end and the digits after decimal places never repeat. For example, when a rational number, say 4/3, is written in decimal form, it converts to 1.33333….., which means that it never ends but digit “3” is repeating. In irrational numbers, these digits do not repeat and thus are unique. π in decimal form is 3.141592……., the digits will never end and they will not repeat. So, digits will go until infinity.
This has led to great interest in π and people who try to memorise the maximum number of digits of π they can. The current world record is held by Suresh Kumar Sharma who, in 2015, recited 70,030 decimal places of π, taking more than 17 hours to do so. Imagine memorising a sequence of digits and reciting them for 17 hours! Using supercomputers, we have calculated the value of π till trillions of digits. In fact, many times the calculation of π is used as a performance test of computer processors.
There is another very interesting inference from the fact that π digits do not end and do not repeat. It implies the digits of π will have every sequence of digits possible in the world. For example, if your mobile number is 9876543210, you will definitely find it in the digits of π. You can find your ATM pin, Aadhar and bank account numbers as well. But because such calculations are very intensive even for computers of the present age, this might not yet be possible. Still, you can try out different combinations of digits on different π-digit search websites that are available on the internet. We have been able to find many seven or eight-digit sequences in π. For example, the sequence “360” is there at the 285th position and “12345678” is at the 186557266th position.
The idea of π has been an inspiration for many movies as well. In the movie Life of Pi, the boy is named “Pi” because he could fill several blackboards with the digits of π from memory. In Star Trek, the heroes have been able to save the world from an evil, artificially intelligent computer from ruling the world by challenging it to calculate the last digit of π, which is an impossible task. The evil computer froze and then exploded.
So, where does 22/7 come from? It is a ratio of two integers and, therefore, a rational number which π clearly is not. The answer is simple, as π has infinite digits, we use an approximate value of π and not the exact value. For practical purposes, 22/7 or 3.14 is a good enough approximation for π.
Due to its multiple uses, π has a fan following as well. Every year, March 14 is celebrated as “Pi-Day” because the date can be written as 3/14, which are the first three digits of π. On this day, Maths enthusiasts try to recite as many digits of π as possible, have parades and eat pie. A language too has also been invented based on π.
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