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# Numbers

B.E. Mechanical Engineering

As much as the ‘words’ have revolutionised mankind, the ‘numbers’ have played equally significant role. Numbers have an edge over words in a sense, both scientifically and psychologically speaking, that numbers are believed to determine everything that lies at the present and in the future. Numbers are fun too; you can add every numbers up to infinity and still get -1/12 as the final result (check for Ramanujan Summantion over internet). So, here’s a list some unique numbers just for the sake of fun and information.

1. The singularity. The very first. You and no other. ‘1’ is a concept before it is a number. Give it a thousand names, but after all, when you have to start the journey to infinity, you always start with one single idea – the idea of ‘just one’.

0: As much as the existence of something buzzes our mind, the concept of nothingness is equally perplexing. As a matter of fact, ancient Greek mathematicians and scholars were in dilemma if ‘nil’ could be counted as a number. They asked themselves “how can ‘nothing’ be something?”.

The use of zero as a number can be found as back as in Mesopotamian and Egyptian civilisation. But, it was in the Sanskrit language where ‘sunya’ was defined more clearly, referring to the concept of void. The documented mathematical use of zero dates back to 628 AD by Brahmagupta. Later, the idea of using zero as a number spread to China and Middle East, and then to the whole world.

2. Fibonacci number is a quite popular sequence of number when it comes to unique numbers. This sequence comprises the numbers starting from 1 and adding previous two numbers, except for the second ‘one’ which is only repeated.

1 1 2 3 5 8 13 21 34 55 89 144 … 3.Perfect number

A perfect number is the sum of all of its proper positive divisors, excluding itself.

It is believed to be first documented by famous Swiss mathematician and physicist Leonhard Euler.

Examples:

6 = 1 + 2 + 3

28 = 1+ 2+ 3+ 4 +5 + 6+ 7

496 = 1 + 2 + 3 + 4 + 5+ … + 29 + 30 + 31

8128 = 1 + 2+ 3+ 4 + 5+ … + 125 + 126 + 127

33550336 = 1 +2 +3+ 4 +5 + … + 8189 + 8190+ 8191

4.Hardy–Ramanujan number

One time British mathematician G. H. Hardy went to visit his friend  Srinivasa Ramanujan. Hardy told Ramanujan that the taxi number, which was 1729, seemed dull to him. Ramanujan told Hardy that it was quite an interesting number. It was the smallest number expressible in as the sum of two cubes of positive numbers in two different way.

1729 = 13 + 123 = 93 + 103

But, if negative cubes are also to include, the smallest such number reduces to 91, which surprisingly is one of the factors of 1729.

91 = 63 + (-5)3 = 33 + 43

Now, here’s what’s more interesting:

1 + 7 + 2 + 9 = 19

19*91 = 1729

5.Kaprekar’s constant

Kaprekar’s constant gets its name from Indian mathematician D. R. Kaprekar. It gets its popularity from its unique feature which is explained in few steps:

1. Take any four digit number, excluding 1111, 2222, 3333, … 9999
2. Arrange the number once in ascending order and again in descending order.
• Subtract the smaller number from the larger number.
1. Repeat these steps for few times. In at most 7 iterations, you’ll get the number 6174.

Do it for yourself for the proof!

6.12 + 3 – 4 + 5 + 67 + 8 + 9 = 100

7.Okay, a game at last. What’s the largest number you can make using only three digits?

999? No, it’s not.

The largest number you can make using 3 digits is 9^9^9.