Why is 1729 called ramanujan number
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Hardy-Ramanujan Number
The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by
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' " (Hofstadter 1989; Kanigel 1991; Snow 1993; Hardy 1999, pp. 13 and 68).
This property of 1729 was mentioned by the character Robert the sometimes insane mathematician, played by Anthony Hopkins, in the 2005 film Proof. It was also part of the designation of the spaceship Nimbus BP-1729 appearing in Season 2 of the animated televisio
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1729 (number)
Natural number
Natural number
| Cardinal | one thousand seven hundred twenty-nine |
|---|---|
| Ordinal | 1729th (one thousand seven hundred twenty-ninth) |
| Factorization | 7 × 13 × 19 |
| Divisors | 1, 7, 13, 19, 91, 133, 247, 1729 |
| Greek numeral | ,ΑΨΚΘ´ |
| Roman numeral | MDCCXXIX, mdccxxix |
| Binary | 110110000012 |
| Ternary | 21010013 |
| Senary | 120016 |
| Octal | 33018 |
| Duodecimal | 100112 |
| Hexadecimal | 6C116 |
1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic numbers in two different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan.
As a natural number
1729 is composite, the squarefree product of three prime numbers 7 × 13 × 19.[1] It has as factors 1, 7, 13, 19, 91, 133, 247, and 1729.[2] It is the third Carmichael number,[3] and the first Chernick–Carmichael number.[a] Furthermore, it is the first in the family of absolute Euler pseudoprim
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Taxi-cab numbers, among the most beloved integers in math, trace their origins to 1918 and what seemed like a casual insight by the Indian genius Srinivasa Ramanujan. Now mathematicians at Emory University have discovered that Ramanujan did not just identify the first taxi-cab number – 1729 – and its quirky properties. He showed how the number relates to elliptic curves and K3 surfaces – objects important today in string theory and quantum physics.
“We’ve found that Ramanujan actually discovered a K3 surface more than 30 years before others started studying K3 surfaces and they were even named,” says Ken Ono, a number theorist at Emory. “It turns out that Ramanujan’s work anticipated deep structures that have become fundamental objects in arithmetic geometry, number theory and physics.”
Ono and his graduate student Sarah Trebat-Leder are publishing a paper about these new insights in the journal Research in Number Theory. Their paper also demonstrates how one of Ramanujan’s formulas associated w