Maths ramanujan

May 3, 2023 3

Srinivasa Ramanujan better known as Srinivasa Iyengar Ramanujan was one of India's greatest mathematical genius. Ramanujan was born in his grandmother's house in Erode 22 December 1887 , a small village about 400 km southwest of Madras. His parents were K. Srinivasa Iyengar and Komalatammal. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km near to Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop.

When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics

Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in 1904.

However the following year his scholarship was not renewed because Ramanujan devoted more and more of his time to mathematics and neglected his other subjects. Without money he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about 650 km north of Madras. He failed in English in Intermediate .

In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras. He attended lectures at Pachaiyappa's College but became ill after three months study. He took the First Arts examination after having left the course. He passed in mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras. Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908. At this stage he became seriously ill again and underwent an operation in April 1909 after which he took him some considerable time to recover.

He married on 14 July 1909 when his mother arranged for him to marry a ten year old girl S Janaki Ammal. Ramanujan did not live with his wife, however, until she was twelve years old.

Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society. After publication of a brilliant research paper on Bernoulli numbers in 1911 in the Journal of the Indian Mathematical Society he gained recognition for his work. Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius.

Ramanujan showed that any big number can be written as sum of not more than four prime numbers.

He showed that how to divide the number into two or more squares or cubes.

when Mr Litlewood came to see Ramanujan in taxi number 1729, Ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways, i.e. 1729 = 93 + 103 = 13 + 123 since then the number 1729 is called Ramanujan’s number.

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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

NOWLETS FACE THE

CLIMAX

RAMANUJAN’S MAGIC SQUARE

22 12 18 87

88 17 9 25

10 24 89 16

19 86 23 11

Do you know date of birth of Srinivasa Ramanujan?

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.

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

1906-1912 Ramanujan continued noting down his results on loose leaf papers

Published three note books of pages 212, 352 and 33 (1967).

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Magic Squares, Sums of Series, Combinational Analysis, Polynomials, Number Theory, Analogues of Gamma Functions, Continued Fractions Elliptic integrals Highly composite numbers Properties of primes.

CONTRIBUTION’S OF RAMANUJAN IN CONTRIBUTION’S OF RAMANUJAN IN DIFFERENT AREAS OF DIFFERENT AREAS OF

MATHEMATICSMATHEMATICS

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