KENDRIYA VIDYALAYA MATHS PROJECT ON HISTORY OF RAMANUJAM AND HIS CONTRIBUTIONS BY SHIVA PRASAD 9 TH A
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KENDRIYA VIDYALAYA
MATHS PROJECTON
HISTORY OF RAMANUJAM AND HIS CONTRIBUTIONS
BYSHIVA PRASAD
9TH A
2
SRINIVASA IYANGAR RAMANUJAN’S LIFE AND HIS GENIUS
1887-1920
Basic Introduction
Born 22 December 1887 Erode, Madras
Presidency
Died 26 April 1920 (aged 32) Chetput,Madras
Presidency
Basic Introduction
o Father : Kuppuswamy Srinivasa Iyengar, a clerical assistant (Gumastha) to a cloth merchant
o Mother: Komalatammal, was a housewife
Basic Introductiono Spouse : Janaki Ammal
o Residence Kumbakonam
o Nationality Indian
o Fields Mathematics
o Alma mater Government Arts College Pachaiyappa's College
o Academic advisors G. H. Hardy J. E. Littlewood
o Signature
6
Srinivasa Ramanujan Said:
7
Srinivasa Ramanujan is known as an all-time great Indian Mathematician
Born on 22 nd
December 1887,Erode,
Tamilnadu, India
8
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
9
SCHOOL EDUCATION
Passed primary examination andStood first in the district at
Town high school-Kumbakonam (1898).
Mastered advanced trigonometry written by S. L. Loney at the age of
13 years.
10
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 .
11
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.
12
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.
13
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
14
SRINIVASA RAMANUJAN
AND HIS MAGIC SQUARE
15
RAMANUJAN’S MAGIC SQUARE
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?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
16
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
17
RAMANUJAN’S MAGIC SQUARE
Sum of numbers of any column is also 139.
Oh, this will be there in any magic square.
What is so great in it..?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
18
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…?
19
RAMANUJAN’S MAGIC SQUARE
Sum of corner numbers is also 139.
Interesting?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
20
RAMANUJAN’S MAGIC SQUARE
Look at these possibilities. Sum of identical coloured boxes is also 139.
Interesting..?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
21
RAMANUJAN’S MAGIC SQUARE
Look at these possibilities. Sum of identical coloured boxes is also 139.
Interesting..?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
22
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…?
23
RAMANUJAN’S MAGIC SQUARE
Can you try these combinations?
Interesting…..?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
24
RAMANUJAN’S MAGIC SQUARE
Try these combinations also?
Interesting.…..?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
25
RAMANUJAN’S MAGIC SQUARE
It is 22nd Dec 1887.
Yes. It is 22.12.1887
BE A PROUD INDIAN
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
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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 .....
Ramanujan himself supplied the solution to the problem
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Deplorable Condition of Ramanujan
“When food is the problem, how can I find money for paper? I may
require four reams of paper every month.”
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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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CONTRIBUTION TO THE THEOREY OF PARTITIONS
• A partition of a natural number ‘n’ is a sequence of non-decreasing positive integers whose sum is ‘n’.
N No. of PARTITIONS
1 1
2 2
3 3
4 5
5 7
6 11
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The highest highly composite number listed by Ramanujan is
6746328388800Having 10080 factors
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
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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 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.
37
We Miss a Great Mathmatician
• 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 nadu)
38
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
39
THANK YOU
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