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SRINIVASA IYANGAR RAMANUJAN’S LIFE AND HIS GENIUS

1887-192004/10/23

Srinivasa Ramanujan Said:

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Srinivasa Ramanujan is known as an all-time great

Indian Mathematician

Born on 22 nd

December 1887,Erode,Tamilnadu, India

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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!

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SCHOOL EDUCATIONPassed primary examination and

Stood first in the district atTown high school-Kumbakonam

(1898).Mastered advanced trigonometry written by S. L. Loney at the age

of 13 years.

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Adulthood He was a self-taught Mathematician. He was really good at Maths so when he took his exam, he passed in Maths, 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.

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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

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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 INDIANBE A PROUD INDIAN

.

Ramanujan himself supplied the solution to

the problem

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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

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Srinivasa Ramanujan at Trinity college,Cambridge

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

Hardy commented that the number 1729 seemed to be unintresting.

Ramanujan said that it is a very intresting mathematical number.

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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

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Largest known similar number is

885623890831 =75113

+77303

=87593+59783

Ramanujan was indeed a friend of numbers.

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CONTRIBUTION TO THE THEOREY OF PARTITIONS

N No. of PARTITIONS

1 1

2 2

3 3

4 5

5 7

6 11

A partition of a natural number ‘n’ is a sequence of non-decreasing positive integers whose sum is ‘n’.04/10/23 Source:

Confidential 29

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 function

The highest highly composite number listed by Ramanujan

is 6746328388800Having 10080 factors

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The last three Books of Ramanujan

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Calculations of Ramanujan in his own handwriting

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Mock Theta Functions

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TOUGH LIFE IN ENGLANDPure 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.

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Ramanujan sailed to Indian on 27 february

1919 and arrived on 13 march

However his health was very poor.

He passed away on 26th April 1920 at

Kumbakonam(Tamil naidu)

We Miss a Great Mathematician

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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

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Prepared by

Charan Kumar Ganteda

MathematicsKL UNIVERSITY

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