Ramanujan’s Math – Magic ! Sowndrarajan. S P.G. & Research Dept. Of Mathematics Raja Doraisingam Govt. Arts College Sivaganga-630561.

OUTLINE Ramanujan’s Life and passion Ramanujan’s Magic Square The man who knew Infinity Radical Brain Teaser Partitions Ramanujan’s Crazy Summation The Taxi Cab Number

Ramanujan’s Life and Passion Born on December 22 , 1887 in Pallipalayam, Erode and grew up in Kumbakonam, Tamil nadu. Son of Srinivas Iyenger and Komalathammal. At the age of 12, he was declared “CHILD MATHEMATICIAN” by his teachers. He did most of his mathematical exploration by his own(In particular he discovered much trigonometry by himself as a 13 years old boy!) He spent many hours in his temple lobby listening to Drums as he did his mathematics. His findings came as visions from his hometown goddess “Namagiri”.

GLORY AND TRAGEDY He found a Clerical job in Madras port to help his family from poverty. (All other free time were spent for maths) Ramanujan wrote many letters to mathematician around the world including one to G.H. Hardy. Hardy invited Ramanujan to Cambridge. During his visit, Ramanujan wrote 30 papers (some on his own, some joint with Hardy) Ramanujan had to overcome many difficulties like world war I, Inability to eat English food. Despite these hardships, for his field-changing work he was elected “Fellow of the Royal Society” Due to Malnutrition, he felt ill, and he returned to home, where he died one year later in 1920 at the Young age of 32.

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

Ramanujan’s Magic Square 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 Sum of numbers of any row is 139. Sum of numbers of any Column is 139.

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

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..? 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 RAMANUJAN’S MAGIC SQUARE

RAMANUJAN’S MAGIC SQUARE 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 22 12 18 87 88 17 9 25 10 24 89 16 19 86 23 11 Can you find Ramanujan Birthday from the square? Yes. It is 22.12.1887

How it Works ? Example: A B C D A B C D D+1 C-1 B-3 A+3 B-2 A+2 D+2 25 08 19 96 87 18 05 28 06 27 88 17 20 85 26 07 SSR’s Birthday Magic Square Its 25. 08. 1986

Ramanujan’s Radical Brain Teaser (1911) What is the value of x in the following equation? Any Guess !

Remarkably the answer is exactly 3. Behold!

Ramanujan’s works with Infinity Ramanujan Summation Problem 1+2+3+4+…………… = ? Is it Infinity! The Hardy-Ramanujan Asymptotic Partition Formula We can partition 4 into 5 different ways ! 4, 3+1, 2+2, 2+1+1,1+1+1+1 P(4)= 5 P(8)=22 P(32)=213 P(96)=8349 P(64)=1741630 P(128)=4351078600 P(256)=365749566870782 He developed a formula for partition of any number (A long time unsolved problem!) -1/12

1729 is a sum of two cubes in two different ways Taxicab Number 1729 equals 13 + 123 equals 93 + 103 1729 is a sum of two cubes in two different ways

Ramanujan’s work