Srinivasa ramanujan

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Srinivasa ramanujan

  1. 1. 02/23/13 Source: Confidential 1
  2. 2. SRINIVASA IYANGAR RAMANUJAN’S LIFE AND HIS GENIUS 02/23/13 1887-1920
  3. 3. Srinivasa Ramanujan Said:02/23/13 Source: Confidential 3
  4. 4. Srinivasa Ramanujan is known as an all-time great Indian Mathematician Born on 22 nd December 1887,Erode, Tamilnadu, India02/23/13 Source: Confidential 4
  5. 5. 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!02/23/13 Sour Confidential 5
  6. 6. SCHOOL EDUCATION Passed primary examination and Stood first in the district at Town high school-Kumbakonam (1898). Mastered advanced trigonometry written by S. L. Loney at the age of 13 years.02/23/13 Source: Confidential 6
  7. 7. Adulthood He was a self-taught Mathematician. He was really good at Maths so whenhe took his exam, he passed in Maths,but failed in other subjects because ofhis disinterest. So , he couldn’t enterthe university of Madras for furtherstudies. He was married with a nine years oldgirl named Janaki Ammal, when hewas 22 but he did not live with his wifetill she reached the age of 12. Since he showed extraordinary talentby himself, people around him helpedto take his achievements known to theother Internationally renownedmathematicians .
  8. 8. 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.02/23/13 Source: Confidential 8
  9. 9. 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.02/23/13 Source: Confidential 9
  10. 10. 02/23/13 Confidential 10
  11. 11. SRINIVASA RAMANUJAN AND HIS MAGIC SQUARE
  12. 12. RAMANUJAN’S MAGIC SQUARE This square looks like any other normal magic22 12 18 87 square. But this is formed by great88 17 9 25 mathematician of our country – Srinivasa10 24 89 16 Ramanujan.19 86 23 11 What is so great in it?
  13. 13. RAMANUJAN’S MAGIC SQUARE Sum of numbers of any row is 139.22 12 18 87 What is so great in it.?88 17 9 2510 24 89 1619 86 23 11
  14. 14. RAMANUJAN’S MAGIC SQUARE Sum of numbers of any column is also 139.22 12 18 87 Oh, this will be there in any magic square.88 17 9 25 What is so great in it..?10 24 89 1619 86 23 11
  15. 15. RAMANUJAN’S MAGIC SQUARE Sum of numbers of any diagonal is also22 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
  16. 16. RAMANUJAN’S MAGIC SQUARE Sum of corner numbers is also 139.22 12 18 87 Interesting?88 17 9 2510 24 89 1619 86 23 11
  17. 17. RAMANUJAN’S MAGIC SQUARE Look at these possibilities. Sum of22 12 18 87 identical coloured boxes is also 139.88 17 9 25 Interesting..?10 24 89 1619 86 23 11
  18. 18. RAMANUJAN’S MAGIC SQUARE Look at these possibilities. Sum of22 12 18 87 identical coloured boxes is also 139.88 17 9 25 Interesting..?10 24 89 1619 86 23 11
  19. 19. RAMANUJAN’S MAGIC SQUARE Look at these central squares.22 12 18 87 Interesting…?88 17 9 2510 24 89 1619 86 23 11
  20. 20. RAMANUJAN’S MAGIC SQUARE Can you try these combinations?22 12 18 87 Interesting…..?88 17 9 2510 24 89 1619 86 23 11
  21. 21. RAMANUJAN’S MAGIC SQUARE Try these combinations also?22 12 18 87 Interesting.…..?88 17 9 2510 24 89 1619 86 23 11
  22. 22. RAMANUJAN’S MAGIC SQUARE It is 22nd Dec 1887.22 12 18 87 Yes. It is 22.12.188788 17 9 2510 24 89 16 BE A PROUD INDIAN19 86 23 11
  23. 23. . Ramanujan himself supplied the solution to the problem3 = 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 +.....02/23/13 Source: Confidential 23
  24. 24. 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.”02/23/13 Source: Confidential 24
  25. 25. Srinivasa Ramanujan at Trinity college,Cambridge02/23/13 Source: Confidential 25
  26. 26. Ramanujan and Hardyarrived at Ramanujan’sresidence in a cabnumber 1729.Hardy commented thatthe number 1729 seemedto be unintresting.Ramanujan said that it isa very intrestingmathematical number.02/23/13 Source: Confidential 26
  27. 27. 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 numbers02/23/13 Source: Confidential 27
  28. 28. Largest known similar number is 885623890831 =75113 +77303 =87593+59783 Ramanujan was indeed a friend of numbers.02/23/13 Source: Confidential 28
  29. 29. CONTRIBUTION TO THETHEOREY OF PARTITIONSA partition of N No. ofa natural PARTITIONSnumber ‘n’ is a 1 1sequence of 2 2 3 3non- 4 5decreasing 5 7positive 6 11integers whosesum is ‘n’.02/23/13 Source: Confidential 29
  30. 30. 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 6746328388800 Having 10080 factors02/23/13 Source: Confidential 30
  31. 31. The last three Books of Ramanujan02/23/13 Source: Confidential 31
  32. 32. Calculations of Ramanujan in his own handwriting02/23/13 Source: Confidential 32
  33. 33. 02/23/13 Source: Confidential 33
  34. 34. 02/23/13 Source: Confidential 34
  35. 35. 02/23/13 Source: Confidential 35
  36. 36. Mock Theta Functions02/23/13 Source: Confidential 36
  37. 37. 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.02/23/13
  38. 38. We Miss a Great Mathematician Ramanujan sailed toIndian on 27 february 1919 and arrived on 13 march However his health was very poor. He passed away on 26th April 1920 atKumbakonam(Tamil naidu)02/23/13 Source: Confidential 38
  39. 39. Recognition by Govt.of IndiaThe Prime Minister of India, Dr. Manmohan Singh has declared the year 2012 as the “NationalMathematical Year” and thedate December 22, being the birthday of Srinivasa Ramanujan has been declared as the National Mathematics02/23/13 Source: Confidential 39
  40. 40. Prepared by Charan Kumar Ganteda Mathematics KL UNIVERSITY02/23/13 40
  41. 41. 02/23/13 Source: Confidential 41

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