1729 (number)
- This article is about the number 1729. For the year AD 1729, see 1729.
1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Aiyangar Ramanujan. In Hardy's words [1]:
| 1729 | |
|---|---|
| Cardinal | One thousand seven hundred [and] twenty-nine |
| Ordinal | 1729th |
| Factorization | |
| Divisors | 7,13,19,91,153,247 |
| Roman numeral | MDCCXXIX |
| Binary | 11011000001 |
| Hexadecimal | 6C1 |
- I remember once going to see him 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."
Two things are to be noted regarding the above anecdote, both of which, unfortunately, take away from the surprise element. Firstly, Ramanujan didn't discover the taxicab property on-the-spot; it has been found in one of his notebooks dated years before the incident. Secondly, Hardy possibly knew it as well, and pretended not to only to cheer up the ailing Ramanujan. Indeed, such behaviour would have been in keeping with Hardy's self-deprecating character. This hypothesis appears more plausible when we consider that 1729 is the third Carmichael number, which makes it unlikely that Hardy would have really thought it "dull".
1729 is a Zeisel number.
1729 has another property -- the 1729th decimal place is the beginning of the first occurrence of all ten digits consecutively in the decimal representation of e, although, of course, this fact would have been unknown to either mathematician, since computers weren't built until much later. [1]
See also
Quote
"Every positive integer is one of Ramanujan's personal friends" -- J. E. Littlewood, on hearing of the taxicab incident.
External links
References