What is Ramanugam Number ? ( Mathamatician)?

Answer 1

Hi,

Ramanujan is known as a number theorist. Hardy was a number theorist but he was also into analysis. When Ramanujan was at Cambridge with Hardy, he was naturally influenced by him (Hardy). And so most of the papers he published while he was in England were in number theory. His real great discoveries are in partition functions.

Along with Hardy, he found a new area in mathematics called probabilistic number theory, which is still expanding. Ramanujan also wrote sequels in highly composite numbers and arithmetical functions. There are half a dozen or more of these papers that ma de Ramanujan very famous. They are still very important papers in number theory.

Ramanujan is also popular for his approximations to pie. Many of his approximations came with his work on elliptic functions. Ramanujan computed what are called class invariants. Even as he discovered them, they were computed by a German mathematician, H . Weber, in the late 19th and early 20th centuries. But Ramanujan was unaware of this. He computed 116 of these invariants which are much more complicated. These have applications not only in approximations to pie but in many other areas as well.

The most famous application in physics is in the area of statistical mechanics. Among those who the world know have used Ramanujan's mathematics extensively is W. Backster, the well-known physicist from Australia. He used the famous Rogers-Ramanujan identities i n what is called the hard hexagon model to describe the molecular structure of a thin film.

Then there is a particular formula of Ramanujan's involving the exponential function which has been used many times in statistics and probability. Ramanujan had a number of conjectures in regard to this formula and one is still unproven. He made this con jecture in a problem he submitted to the Indian Mathematical Society. The asymptotic formula is used, for instance, in the popular problem: What is the minimum number of people you can have in a room so that the probability that two share a common birthd ay is more than half? it is 21, 22 or 23. Anyway, this problem can be generalised to many other types of similar problems.

To much of the mathematical world and to the public in general, Ramanujan is known as a number theorist. Hardy was a number theorist but he was also into analysis. When Ramanujan was at Cambridge with Hardy, he was naturally influenced by him (Hardy). And so most of the papers he published while he was in England were in number theory. His real great discoveries are in partition functions.

Along with Hardy, he found a new area in mathematics called probabilistic number theory, which is still expanding. Ramanujan also wrote sequels in highly composite numbers and arithmetical functions. There are half a dozen or more of these papers that ma de Ramanujan very famous. They are still very important papers in number theory.

The area in which Ramanujan spent most of his time, more than any other, is in elliptic funct ions (theta functions), which have strong connections with number theory. In particular, Chapters 16 to 21 of the second notebook and most of the unorganised portions of the notebooks (ramanjams) are on theta functions. There is a certain type of theta functions ide ntity which has applications in other areas of mathematics, particularly in number theory, called modular equations. Ramanujan devoted an enormous amount of effort on refining modular equations.

Ramanujan is also popular for his approximations to pie. Many of his approximations came with his work on elliptic functions. Ramanujan computed what are called class invariants. Even as he discovered them, they were computed by a German mathematician, H . Weber, in the late 19th and early 20th centuries. But Ramanujan was unaware of this. He computed 116 of these invariants which are much more complicated. These have applications not only in approximations to pie but in many other areas as well.

Then there is a particular formula of Ramanujan's involving the exponential function which has been used many times in statistics and probability. Ramanujan had a number of conjectures in regard to this formula and one is still unproven. He made this con jecture in a problem he submitted to the Indian Mathematical Society. The asymptotic formula is used, for instance, in the popular problem: What is the minimum number of people you can have in a room so that the probability that two share a common birthd ay is more than half? I think it is 21, 22 or 23. Anyway, this problem can be generalised to many other types of similar problems.

Actually the famous Ramanujam number 1729. (The number plate of the taxi used by Ramanujam when he went to see Hardy, bore the number 1729. The genius in Ramanujam at once discovered its uniqueness. He explained to Hardy that it was the lowest number, which could be expressed in 2 ways, as the sum of cubes of a pair of numbers (1729= 93+103 and also13+123).

Ramanjuam was one of the hundreds of famous scientists mother Indian produced.

Answer 2

Mr. Jitleo has given a very comprehensive answer to the question, describing the entire history behind the question. Ramanujam was perhaps the first to point out that 1729 is the smallest number that can be expressed as sum of two cubes in two different ways. That is 9^3 + 10^3 = 12^3 + 1^3 = 1729. ( i.e. 9 cubed plus 10 cubed is equal to 12 cubed plus 1 cubed). The next such number is a five digit number.

Answer 3

1729 = 10^3 + 9^3 = 1^3 + 12^3
= 1000+729 = 1 + 1728

Answer 4

G H Hardy, Ramanujan's contemporary and 'mentor' wrote:
"I remember once going to see Ramanujan when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. 'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'"
In honour of Ramanujan, the number 1729 is called Ramanujan's number.

Answer 5

1729

Answer 6

1729

Answer 7

1729.


Doug

Answer 8

zero, he was the inventor of it, this piece of info is not only from indian history but from german and french literature also.

Answer 9

why do you want his mobile number... he s no more in this earth.................:)................