srinivasa ramanujan a great indian mathematician
TRANSCRIPT
BORN 22 December 1887
PLACE OF BIRTH ERODE, TAMILNADU
FATHER K. Srinivasa Iyengar
MOTHER Komalat Ammal
WIFE Janaki Ammal
SIBLINGS Sadagopan
&
HE STARTED HIS SCHOOLING IN 1892. INITIALLY HE DID NOT LIKE SCHOOL THOUGH HE SOON STARTED EXCELLING HIS STUDIES, ESPECIALLY MATHEMATICS.
IN 1897 HE PASSED HIS EXAMS IN ENGLISH, TAMIL, GEOGRAPHY
AND ARITHMETIC WITH THE HIGHEST SCORES IN HIS
DISTRICT.
ONCE HIS TEACHER SAID THAT WHEN ZERO IS DIVIDED BY ANY NUMBER, THE RESULT IS
ZERO, RAMANUJAN IMMEDIATELY ASKED HIS TEACHER WHEATHER ZERO DIVIDED BY ZERO
GIVES ZERO.
HE PASSED HIS PRIMARY EXAMINATIONS AND STOOD FIRST IN THE DISTRICT AT
TOWN HIGH SCHOOL-KUMBAKONAM IN1898
HE ALSO MASTERED ADVANCED TRIGONOMETRY WRITTEN BY S.L. LONEY AT THE AGE OF 13 YEARS.
IN HIGH SCHOOL HE DEVOURED BOOKS ON MATHEMATICS AND
DISCOVERED ADVANCED THEOREMS.
AT THE AGE OF 16 HE GOT HIS HANDS ON A BOOK CALLED ‘A
SYNOPSIS OF ELEMENTARY RESULTS IN PURE AND APPLIED MATHEMATICS’ BY G.S. CARR WHICH WAS A COLLECTION OF
5,000 THEOREMS. HE WAS THOROUGHLY FASCINATED BY
THE BOOK AND SPENT MONTHS STUDYING IT IN DETAIL. THIS BOOK IS CREDITED TO HAVE
AWAKENED THE MATHEMATICAL GENIUS IN HIM
BY THE TIME HE WAS 17, HE HAD INDEPENDENTLY
DEVELOPED AND INVESTIGATED THE BERNOULLI
NUMBERS AND HAD CALCULATED THE EULER–
MASCHERONI CONSTANT UP TO 15 DECIMAL
PLACES. HE WAS NOW NO LONGER INTERESTED IN
ANY OTHER SUBJECT, AND TOTALLY IMMERSED
HIMSELF IN THE STUDY OF MATHEMATICS ONLY.
HE WAS GRADUATED FROM TOWN HIGH SECONDARY SCHOOL
IN 1904 AND WAS AWARDED THE K. RANGANATHA RAO PRIZE
FOR MATHEMATICS BY THE SCHOOL'S HEADMASTER,
KRISHNASWAMI IYER.
RAMANUJAN MADE SUBSTANTIAL
CONTRIBUTIONS TO THE
ANALYTICAL THEORY OF NUMBERS
AND WORKED ON ELLIPTIC FUNCTIONS,
CONTINUED FRACTIONS AND INFINITE. IN 1900 HE BEGAN TO WORK ON HIS OWN ON
MATHEMATICS SUMMING GEOMETRIC AND
ARITHMETIC SERIES.
HE WORKED ON DIVERGENT SERIES.
HE SENT 120 THEOREMS ON SIMPLE
DIVISIBILITY PROPERTIES OF THE
PARTITION FUNCTION.
PARTITION OF WHOLE NUMBERS IS ANOTHER
SIMILAR PROBLEM THAT CAPTURED
RAMANUJAN’S ATTENTION.
SUBSEQUENTLY RAMANUJAN DEVELOPED A
FORMULA FOR THE PARTITION OF ANY
NUMBER, WHICH CAN BE MADE TO YIELD THE
REQUIRED RESULT BY A SERIES OF
SUCCESSIVE APPROXIMATION.
EXAMPLE 3=3+0=1+2=1+1+1.
GOLDBACH’S CONJECTURE
IT IS ONE OF THE MOST IMPORTANT
ILLUSTRATIONS OF RAMANUJAN CONTRIBUTION
TOWARDS THE PROOF OF THE CONJECTURE.
THE STATEMENT IS EVERY EVEN INTEGER
GREATER THAT TWO IS THE SUM OF TWO
PRIMES.
THAT IS, 6=3+3RAMANUJAN AND HIS ASSOCIATES HAD
SHOWED THAT EVERY LARGE INTEGER COULD
BE WRITTEN AS THE SUM OF AT MOST FOUR
(EXAMPLE: 43=2+5+17+19).
RAMANUJAN STUDIED THE HIGHLY
COMPOSITE NUMBERS ALSO
WHICH ARE RECOGNIZED AS THE
OPPOSITE OF PRIME NUMBERS.
HE STUDIED THEIR STRUCTURE,
DISTRIBUTION AND SPECIAL
FORMS
NUMBERS
FERMAT THEOREM
HE ALSO DID CONSIDERABLE WORK ON
THE UNRESOLVED FERMAT THEOREM,
WHICH STATES THAT A PRIME NUMBER
OF THE FORM 4m+1 IS THE SUM OF
TWO SQUARES.
RAMANUJAN’S NUMBER
1729 IS A FAMOUS RAMANUJAN
NUMBER.
IT IS THE SMALLEST NUMBER
WHICH CAN BE EXPRESSED AS
THE SUM OF TWO CUBES IN
TWO DIFFERENT WAYS
1729 = 13 + 123 = 93 + 103
CUBIC EQUATIONS AND QUADRATIC
EQUATIONS
RAMANUJAN SHOWED HOW TO SOLVE
CUBIC EQUATIONS.
IN 1902 HE WENT ON TO FIND HIS OWN
METHOD TO SOLVE THE QUADRATIC.
EULER’S CONSTANT
BY 1904 RAMANUJAN HAD
BEGAN TO UNDERTAKE DEEP
RESEARCH.
HE INVESTIGATED THE SERIES
(1/n) AND CALCULATED EULER’S
CONSTANT UPTO 15 DECIMAL
PLACES.
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.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of numbers of any row is
139.
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.
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.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of corner numbers is
also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of these identical
coloured boxes is also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of these identical
coloured boxes is also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum Of Central Squares Is
Also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of these combinations
is also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Sum of these
combinations is
also 139.
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
Do you Remember the birth
of Srinivasa Ramanujan?
22 12 18 87
88 17 9 25
10 24 89 16
19 86 23 11
It is 22-12-1887
(22nd December 1887)
RAMANUJAN'S HOME STATE
TAMIL NADU CELEBRATES 22 DECEMBER
AS STATE I. T. DAY, MEMORIALISING BOTH
THE MAN AND HIS ACHIEVEMENTS, AS A
NATIVE OF TAMIL NADU.
A STAMP PICTURING RAMANUJAN WAS
RELEASED BY THE GOVERNMENT OF INDIA IN
1962 – THE 75th ANNIVERSARY OF RAMANUJAN'S
BIRTH COMMEMORATING HIS ACHIEVEMENTS IN
THE FIELD OF NUMBER THEORY,AND A NEW
DESIGN WAS ISSUED ON 26 DECEMBER 2011, BY
THE INDIAN POSTAL DEPARTMENT.
THE DEPARTMENT OF MATHEMATICS
CELEBRATES THE BIRTH DAY OF RAMANUJAN
BY ORGANISING A
NATIONAL SYMPOSIUM ON MATHEMATICAL
METHODS AND APPLICATIONS
(NSMMA) FOR ONE DAY BY INVITING EMINENT
INDIAN AND FOREIGN SCHOLARS.
ON THE 125TH ANNIVERSARY OF HIS BIRTH, INDIA
DECLARED THE BIRTHDAY OF RAMANUJAN AS
NATIONAL MATHEMATICS DAY.
THE DECLARATION WAS MADE BY
DR. MANMOHAN SINGH IN 2011.
DR. MANMOHAN SINGH ALSO DECLARED THAT THE
YEAR 2012 WOULD BE CELEBRATED AS
THE NATIONAL MATHEMATICS YEAR.
SCULPTURE
OF RAMANUJAN WAS
INSTALLED AT THE
GARDEN OF BIRLA
INDUSTRIAL &
TECHNOLOGICAL
MUESEUM BY ITS
MANAGEMENT.
GOOGLE HONOURED HIM ON
HIS 125TH BIRTH
ANNIVERSARY BY REPLACING
ITS LOGO WITH A DOODLE ON
ITS HOME PAGE.
SRINIVASA RAMANUJAN WAS A SELF-TAUGHT PURE MATHEMATICIAN.
HE HAD TO DROP OUT OF COLLEGE AS HE WAS UNABLE TO GET THROUGH HIS
COLLEGE EXAMINATIONS.
WITH NO JOB AND COMING FROM A POOR FAMILY, LIFE WAS TOUGH FOR HIM AND HE HAD
TO SEEK THE HELP OF FRIENDS TO SUPPORT HIMSELF WHILE HE WORKED ON HIS
MATHEMATICAL DISCOVERIES AND TRIED TO GET IT NOTICED FROM ACCOMPLISHED
MATHEMATICIANS.
HE WROTE A LETTER TO G.H. HARDY CONTAINING 120 THEOREMS WHICH
BROUGHT HIM TO LONDON.
HE WAS THE FIRST INDIAN MATHEMATICIAN TO BE SELECTED IN THE ROYAL SOCIETY OF LONDON.
HE WAS THE SECOND INDIAN TO BE THE MEMBER OF ROYAL SOCIETY OF LONDON AFTER
CURSETJEE
UNFORTUNATELY THIS GREAT
MATHEMATICIAN AND FRIEND OF
NUMBERS DIED ON APRIL 26TH 1920 .
AT CHETPUT IN CHENNAI DUE TO
TUBERCULOSIS AT THE AGE OF 32.
BY: ADNAN ALI KHAN &
MUAAZ FAIYAZUDDIN
IX ‘A’
OF
K.V.N.H.S