ATM pin | Cash Dispensing Method

Everyone in this digital world has a ATM card. There are two things in a ATM which is of vital importance. ATM pin Cash Dispensing Method. L...

Everyone in this digital world has a ATM card.

There are two things in a ATM which is of vital importance.

1. ATM pin
2. Cash Dispensing Method.

Lets talk about these things.

ATM PINS:

We use a four digit number as the pin or password for it.

Researchers and mathematicians were actually thinking of keeping a 6 or 8-digit numbers as the pin for ATM cards. But one man suggested that it is ok that we can use a 4-digit pin. Even if two people has same pin numbers there is no problem in it.

Since everyone is going to choose their unique pin number there will be only lesser chances for robbery and crimes.

If it was not for him we all would be tapping a 6–8 digit number in our ATM.

It was John Shepherd Barron. He was the one to introduce ATM to the world.

So how does the ATM works?

How is it so accurate on dispensing cash?

All ATM we use works on Ramanujan's partition principle.

John studied about this and was astonished and introduced this system.

CASH DISPENSING METHOD:

It was based on the principle of the man who knew infinity.

Very few know this and knows his work.

So I have made a small study on the application of Ramanujan’s partition principle in ATM.

Whenever we insert an ATM card into the ATM, we ask the machine to dispense cash, and it dispenses the cash by counting the money and it dispenses cash very precisely.

Here is the genius work came into play.

He was one of the greatest mathematicians of all time.

A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4)=5$p(4)=5$ because 4 can be written as 1+1+1+1$1+1+1+1$,1+1+2$1+1+2$, 2+2$2+2$, 1+3$1+3$, or 4$4$. The problem of finding p(n) was studied by Euler, who found a formula for the generating function of p(n)$p(n)$ (that is, for the infinite series whose nth term is p(n)x(n)$p(n)x(n)$. While this allows one to calculate p(n)$p(n)$ recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p(n)$p(n)$)

The partition formula is given by:

The formula is so precise. The error for p(1000)$p(1000)$ was about 1.4%.

If it was not for Ramanujan we would not be using ATM today.

Source: Google

Thank you.

Edit 1: Thank you guys for the support. Most people asked me to elaborate the principle ,so here it is. Keep reading.

Edit 2: Guys there is nothing to do with ATM pins and Sir Ramanujan.Its about the cash dispensing method. So if I had misguided you by mentioning about the pin introduced by Sir John Shepherd Barron,I apologize.

For similar things check out my blog The Nerd

~Srinivas Nambi.