Shresth Shukla

  Hello Aliens, This blog is about the very famous Partition theory of numbers by Srinivasa Ramanajun and GH hardy.  The theory of partitions of numbers is an interesting branch of number theory. The concept of partitions was given by Leonard Euler in the 18th century. After Euler though, the theory of partition had been studied and discussed by many other prominent mathematicians like Gauss, Jacobi, Schur, McMahon, and Andrews, etc. but the joint work of Ramanujan with Prof. G.H. Hardy made a revolutionary change in the field of partition theory of numbers. Ramanujan and Hardy invented the circle method which gave the first approximations of the partition of numbers beyond 200. A partition of a positive integer ‘ n’  is a non-increasing sequence of positive integers, called parts, whose sum equals  n . In simpler words, it means the number of ways in which a given number can be expressed as a sum of positive integers.  For example, p(4) = 5, i.e. there are fiv...

Hello Aliens. Well, let me ask you a question before starting my blog. Can you find the total number of factors of any number? For example, let us consider the number 4. We know that the factors of number 4 are (1,2,4). But what if I ask you to find the total number of factors of any bigger number.   Let's say you are supposed to find the total number of divisors of number 2500. Now of course you won't sit and try all the numbers which divide them and then count them. Instead, here we have a simple formula, for that. But before let's have a look at the example below. we can write 2500, as  Now factorizing 2500 into a product of prime numbers. We get. So now we can see that it has been factorized into a product of its prime factors. So here we just have to add "+1" to the powers of the number and then multiply it to give the total number of positive divisors of the number. That is,                    ...

Hello you aliens! Welcome to another blog on one of the most famous symbols in the world of mathematics.  That is  Pi (  π  ).  We all know that Pi is defined as the ratio of the circumference to the diameter of the circle, and is numerically equal to  3.141592653589793238...... and so more. But here we have more interesting facts about Pi  that most of you might not be aware of.Lets have a look on them. 1. Pi ( π ) is an irrational number. That means, it cannot be expressed as a fraction of two integers  (p/q, where q is a non zero integer).  In the 1760s, Johann Heinrich Lambert proved that the  number π  ( pi ) is  irrational. Its an endless number, where you can find about 200 millions digits of Pi. You need a bit mathematical knowledge to understand the image below. 2. We all know that we generally use 22/7 as value of Pi. But, u should know that exact value of Pi is not equal to 22/7 but it is less than 22/7    ...