why came in sets the ramanjun number {1,7,2,9}
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1729 is known as the Ramanujan Number.
This number can be expressed as the sum of 2 cubes.
1729 = 1 ³ + 12³
= 1 + 1728
= 1729
1729 = 9³ + 10³
= 729 + 1000
= 1729
This number can be expressed as the sum of 2 cubes.
1729 = 1 ³ + 12³
= 1 + 1728
= 1729
1729 = 9³ + 10³
= 729 + 1000
= 1729
Answered by
2
What I’ve been doing all morning is that I’ve been trying to come up with some numerically interesting factoid about the number 125. It’s what you get when you cube 5 (5 x 5 x 5, or 5³, but that’s kind of ordinary, no? Well, you can write it as the sum of two squares in two different ways:
2 x 2 + 11 x 11 = 4 + 121 = 125
5 x 5 + 10 x 10 = 25 + 100 = 125
Now that’s promising. But is 125 the smallest number that can be so expressed? No, because 65 is the sum of the squares of 1 and 8, as well as the squares of 4 and 7.
Hmm. May be 125 is the smallest cube that can be written as the sum of two squares in two different ways? It certainly is! Now we’re talking!
Yet what exactly are we talking? And why am I pursuing this pointless pastime?
Well, the great mathematician Srinivasa Ramanujan would have been 125 tomorrow, 22 December. Mathematicians all over India—and indeed the world—are celebrating his life. Delhi, for example, hosted a major international Ramanujan conference this week. And I suspect, all who attended—anyone, in fact, who knows something about Ramanujan—will know the story about him that prompted my quest with 125.
This story: he was in hospital in Putney, England. In walked G.H. Hardy, his mentor and a fine mathematician in his own right. He told Ramanujan that he had come in a cab whose number, 1729, “seemed to me rather a dull one.” (I get the feeling Hardy and Ramanujan rather liked playing around with numbers.)
The sick Ramanujan disagreed. “Oh no, not at all!” he said. “It is the smallest number that can be written as the sum of two cubes in two different ways!”
Of course he was right. Here are the two ways:
1³ + 12³ = 1 + 1,728 = 1,729
9³ + 10³ = 729 + 1,000 = 1,729
2 x 2 + 11 x 11 = 4 + 121 = 125
5 x 5 + 10 x 10 = 25 + 100 = 125
Now that’s promising. But is 125 the smallest number that can be so expressed? No, because 65 is the sum of the squares of 1 and 8, as well as the squares of 4 and 7.
Hmm. May be 125 is the smallest cube that can be written as the sum of two squares in two different ways? It certainly is! Now we’re talking!
Yet what exactly are we talking? And why am I pursuing this pointless pastime?
Well, the great mathematician Srinivasa Ramanujan would have been 125 tomorrow, 22 December. Mathematicians all over India—and indeed the world—are celebrating his life. Delhi, for example, hosted a major international Ramanujan conference this week. And I suspect, all who attended—anyone, in fact, who knows something about Ramanujan—will know the story about him that prompted my quest with 125.
This story: he was in hospital in Putney, England. In walked G.H. Hardy, his mentor and a fine mathematician in his own right. He told Ramanujan that he had come in a cab whose number, 1729, “seemed to me rather a dull one.” (I get the feeling Hardy and Ramanujan rather liked playing around with numbers.)
The sick Ramanujan disagreed. “Oh no, not at all!” he said. “It is the smallest number that can be written as the sum of two cubes in two different ways!”
Of course he was right. Here are the two ways:
1³ + 12³ = 1 + 1,728 = 1,729
9³ + 10³ = 729 + 1,000 = 1,729
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