2.  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.

3.  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

4.  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 .

5.  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.

6.  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.

7.  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.

8. 8

9. 9

10. SRINIVASA RAMANUJAN
AND HIS MAGIC
SQUARE

11. RAMANUJAN’S MAGIC SQUARE
This square looks like
any other normal magic
22 12 18 87
square. But this is
88 17 9 25 formed by great
mathematician of our
10 24 89 16 country – Srinivasa
Ramanujan.
19 86 23 11
What is so great in it?

12. RAMANUJAN’S MAGIC SQUARE
Sum of numbers of
any row is 139.
22 12 18 87
88 17 9 25 What is so great in it.?
10 24 89 16
19 86 23 11

13. RAMANUJAN’S MAGIC SQUARE
Sum of numbers of
any column is also 139.
22 12 18 87
Oh, this will be there in
88 17 9 25 any magic square.
10 24 89 16 What is so great in it..?
19 86 23 11

14. RAMANUJAN’S MAGIC SQUARE
Sum of numbers of
any diagonal is also
22 12 18 87
139.
88 17 9 25
Oh, this also will be there
in any magic square.
10 24 89 16
What is so great in it…?
19 86 23 11

15. RAMANUJAN’S MAGIC SQUARE
Sum of corner
numbers is also 139.
22 12 18 87
Interesting?
88 17 9 25
10 24 89 16
19 86 23 11

16. RAMANUJAN’S MAGIC SQUARE
Look at these
possibilities. Sum of
22 12 18 87
identical coloured
88 17 9 25 boxes is also 139.
Interesting..?
10 24 89 16
19 86 23 11

17. RAMANUJAN’S MAGIC SQUARE
Look at these
possibilities. Sum of
22 12 18 87
identical coloured
88 17 9 25 boxes is also 139.
Interesting..?
10 24 89 16
19 86 23 11

18. RAMANUJAN’S MAGIC SQUARE
Look at these central
squares.
22 12 18 87
Interesting…?
88 17 9 25
10 24 89 16
19 86 23 11

19. RAMANUJAN’S MAGIC SQUARE
Can you try these
combinations?
22 12 18 87
88 17 9 25 Interesting…..?
10 24 89 16
19 86 23 11

20. RAMANUJAN’S MAGIC SQUARE
Try these
combinations also?
22 12 18 87
88 17 9 25 Interesting.…..?
10 24 89 16
19 86 23 11

21. RAMANUJAN’S MAGIC SQUARE
22 12 18 87
NOW
88 17 9 25
LETS
10 24 89 16
FACE
19 86 23 11
THE
CLIMAX

22. RAMANUJAN’S MAGIC SQUARE
Do you know date of
birth of Srinivasa
22 12 18 87
Ramanujan?
88 17 9 25
10 24 89 16
19 86 23 11

23. RAMANUJAN’S MAGIC SQUARE
It is 22nd Dec 1887.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11

24. RAMANUJAN’S MAGIC SQUARE
It is 22nd Dec 1887.
22 12 18 87
88 17 9 25 Yes. It is 22.12.1887
10 24 89 16
BE A PROUD
19 86 23 11 INDIAN

25.  1906-1912 Ramanujan continued
noting down his results on loose leaf
papers
 Published three note books of
pages 212, 352 and 33 (1967).
25

26. CONTRIBUTION’S OF RAMANUJAN IN
DIFFERENT AREAS
 Magic Squares, MATHEMATICS
OF
 Sums of Series,
 Combinational Analysis,
 Polynomials,
 Number Theory,
 Analogues of Gamma Functions,
 Continued Fractions
 Elliptic integrals
 Highly composite numbers
 Properties of primes.
26

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