Hardy-Ramanujan number

Hardy-Ramanujan number

1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:
I remember once going to see him when he was 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 unfavourable 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."

1. Hardy-Ramanujan Number

2. Srinivasa Ramanujan was a person who really knew Infinity or knew more than infinity. He contributed theorems and independently compiled 3,900 results (mostly identities and equations). However, inquisitive minds and those dabbling in mathematical science would also know him for the Hardy-Ramanujan number . Srinivasa Ramanujan

3. The smallest nontrivial   taxicab number , i.e., the smallest number representable in two ways as a sum of two  cubes . It is given by  

4. History The number derives its name from the following story G. H. Hardy told about Ramanujan. "Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,' adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, 'it is a very interesting number. It is the smallest number expressible as the sum of two [ positive ] cubes in two different ways' "

5. Taxicab Number

6. In  mathematics , the  n th  taxicab number , typically denoted Ta( n ) or Taxicab( n ), also called the  n th  Hardy–Ramanujan number , is defined as the smallest integer that can be expressed as a sum of two  positive   integer cubes  in  n  distinct ways. The most famous taxicab number is  1729  = Ta(2) = 1 3  + 12 3  = 9 3  + 10 3 . The name is derived from a conversation in about 1919 involving  mathematicians   G. H. Hardy  and  Srinivasa Ramanujan .

7. Known Taxicab Numbers

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