 Hello friends, so in the previous session we saw that the circumference of a circle divided by diameter of the circle is always a constant and We know from our previous knowledge that this constant is equal to pi This constant is equal to pi so this session is dedicated towards some information about pi now pi is an irrational number So what is an irrational number? It cannot be expressed in the form of a Ratio of two integers Okay, so it's an irrational number so hence it cannot be expressed as a fraction It's decimal representation is not recurring and not terminating, right? This is we know that number is irrational if it's decimal representation is not recurring or non-terminating now pi value is You know 3.1415 92658 goes on it gives Random digits here. It's very difficult to find a trend in the digits of pi hence it's an irrational number Approximate values of pi is also 22 by 7 so many times there is an people make an error and they equate 22 by 7 To pi but it's wrong Actually pi is approximate values 22 by 7 the you know for all practical purposes in our day-to-day calculations We can't really use this number for calculation. So hence we have approximated pi So pi is approximately equal to 22 by 7. It's correct to only two decimal places now there are there are many more accurate value of pi and Another one is 355 upon 133. It's correct to six decimal places and that's good enough for again most of scientific and engineering applications One upon pi is 0.3183. This is another good information because you will see pi into 1 pi pi is approximately equal to 10 so many a dimes We use this Calculation right pi into 1 by pi is approximately equal to So I'm writing pi into 1 1 upon pi is Approximately equal to 10 so we use this Calculation you know this we use this for simplicity of calculation now is pi is called Archimedes principle Sorry, I Archimedes is constant now Archimedes was a third century BC Philosopher scientist he created an algorithm to calculate pi as early as 300 BC now the value of pi is not restricted to only Greeks actually there are lots of evidences which show that pi was being used in Egyptian civilization misopotamia and all where Closest approximation of pi were used So one closest approximation was 25 upon 8. So people were using pi since long long time Now there are these expressions of pi. So, you know pi is Circumference divided by diameter of a circle Those who know integration They will those who have knowledge of calculus. They also know that pi is nothing but when you integrate one upon one minus X square under root so and the limits are minus 1 to 1 Then you get pi again so these are Different expressions now pi has been expressed as continued fraction as well. So here is an example where it is Express as a continued fraction and If you see all the approximations of pi all the fractional approximations of pi has been achieved by equating Some part as zero. So for example in this case if I equate let us say this is very small Very small number So if I if I if I take this as zero then this value becomes three plus one upon seven Which today we use as 22 upon seven, isn't it? So these this is used for you know, approximately finding a fraction approximately equal to pi. So that is Continued fraction. Now, there are multiple other continued fractions in which you can express pi So pi is also four upon one plus one square upon three plus two square upon five So one and so forth. This is one continued fraction. Another one is this So these are the various known continued fractions which Whose value is equal to pi? Now, there are many techniques to find out pie There are there are lots of applications of pi as well in science and mathematics and especially physics In electrostatics and other other such topics you have seen that pi is used Extensively in wave mechanics as well pi is used extensively So pi has got a lot of applications in multiple areas of science. So hence it is Good to know pi a little bit. So hence the session was for that Thanks