1887-1920

SRINIVASA IYANGAR RAMANUJAN’S LIFE AND HIS GENIUS

Srinivasa Ramanujan Said:

Srinivasa Ramanujan is known as an all-time great Indian Mathematician

Born on 22 nd

December 1887,Erode,Tamil Nadu, India

LIFE AND HIS GENIUS

A thought of 7 years Old Ramanujan

Once his teacher said that when zero is divided by any number, the result

is zero, Ramanujan immediately asked his teacher, whether zero divided by zero gives zero; This shows early

signs of his genius!

A thought of 7 years Old Ramanujan

Once his teacher said that when zero is divided by any number, the result is zero, Ramanujan immediately asked his teacher, whether zero divided by zero gives zero; This shows early signs of his genius!

SCHOOL EDUCATION

Passed primary examination andStood first in the district atTown high school- Kumbakonam

(1898).Mastered advanced trigonometry

written by S. L. Loney at the age of 13 years.

Adulthood He was a self-taught Mathematician. He was really good at Math so when he took

his exam, he passed in Math, but failed in other subjects because of his disinterest. So , he couldn’t enter the university of Madras for further studies.

He was married with a nine years old girl named Janaki Ammal, when he was 22 but he did not live with his wife till she reached the age of 12.

Since he showed extraordinary talent by himself, people around him helped to take his achievements known to the other Internationally renowned mathematicians .

He was invited to England to improve his works by G.H.Hardy and J.E Littlewood, who were great mathematicians.

Hardy and Ramanujan had two opposite personalities. As Hardy was an atheist and believes mathematical proof and analysis, Ramanujan was a deeply religious guy and he believed in his trustworthy intuition .

He was the first elected Mathematician from India to the London Mathematical society and he became a Fellow of the Royal society.

Recognition of his Genius

Initially, G. H. Hardy thought

that the works of Ramanujan were

fraud because most of them

were impossible to believe. But

eventually ,they were convinced

and interested in his talent.

Best Known For Landau–Ramanujan

constant Mock theta functions Ramanujan conjecture Ramanujan prime Ramanujan–Soldner

constant Ramanujan theta function Ramanujan's sum Rogers–Ramanujan

identities Ramanujan's master

theorem

SRINIVASA RAMANUJAN

AND HIS MAGIC SQUARE

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

This square looks like any other normal magic square. But this is formed by great mathematician of our country – Srinivasa Ramanujan.

What is so great in it?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Sum of numbers of any row is 139.

What is so great in it.?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Sum of numbers of any column is also 139.

Oh, this will be there in any magic square.

What is so great in it..?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Sum of numbers of any diagonal is also 139.

Oh, this also will be there in any magic square.

What is so great in it…?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Sum of corner numbers is also 139.

Interesting?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Look at these possibilities. Sum of identical coloured boxes is also 139.

Interesting..?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Look at these possibilities. Sum of identical coloured boxes is also 139.

Interesting..?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Look at these central squares.

Interesting…?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Can you try these combinations?

Interesting…..?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Try these combinations also?

Interesting.…..?

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

It is 22nd Dec 1887.

Yes. It is 22.12.1887

BE A PROUD INDIAN

Ramanujan himself supplied the solution to the problem

3 9 1 8 1 2.4

1 2 16 1 2 1 15

1 2 1 3.5 1 2 1 3 25

1 2 1 3 1 24 1 2 1 3 1 4.6

1 2 1 3 1 4 1 35 ..........

1 2 1 3 1 4 1 5 1 .....

“When food is the problem, how can I

find money for paper? I may require four reams of paper

every month.”

Deplorable Condition of Ramanujan

Srinivasa Ramanujan at Trinity College, Cambridge

Ramanujan and Hardy arrived at Ramanujan’s residence in a cab number 1729.

Hardy commented that the number 1729 seemed to be uninteresting.

Ramanujan said that it is a very interesting mathematical number.

The smallest natural number can be represented in two

different ways as a sum of two cubes:

1729=13 +123

=93 +103

It is also incidentally the product of three prime numbers

Largest known similar number is

885623890831 =75113 +77303

=87593+59783

Ramanujan was indeed a friend of numbers.

CONTRIBUTION TO THE THEOREY OF PARTITIONS

N No. of PARTITIONS

1 12 23 34 55 76 11

A partition of a natural number ‘n’ is a sequence of non-decreasing positive integers whose sum is ‘n’.

Example:For N=4,PARTITIONS are

4 = 4 =1+3 =2+2

=1+1+2 =1+1+1+1

P(4)=5,Whether P is a partition functionThe highest highly composite

number listed by Ramanujan is 6746328388800

Having 10080 factors

The last three Books of Ramanujan

Calculations of Ramanujan in his own handwriting

Mock Theta Functions

TOUGH LIFE IN ENGLAND Pure vegetarian meals was not

available. Too busy with calculations and

very often neglected food and spent till late night.

The cold and damp climate disturbed his health.

He was attacked by Tuberculosis.

He returned to India.

Ramanujan sailed to Indian on 27 February 1919 and arrived on 13 marchHowever his health was very poor.He passed away on 26th April 1920 at Kumbakonam (Tamil Naidu)

We Miss a Great Mathematician

Recognition by Govt.of India

The Prime Minister of India, Dr. Manmohan Singh has declared the year 2012 as the “National Mathematical Year” and the date December 22, being the birthday of Srinivasa Ramanujan has been declared as the

National Mathematics day” to be celebrated every year

Name - RISHABH JAINClass -IX – CRoll No - 30