Why is the number 1729 famous ? Well, it all started from around a century back. There were these 2 famous mathematicians, G Hardy and Srinivasa Ramanujam (who was entirely untrained, but a remarkable mathematician) who were sitting in a hospital room (Hardy had come to visit Ramanujam).
Ramanujam asked Hardy about the taxi number that he came in, and Hardy mentioned 1729, calling it a boring number. Ramanujam disputed that,calling 1729 as a very interesting number, it is the smallest number expressible as the sum of two cubes in two different ways.
Which are the 2 ways?
10X10X10 + 9X9X9 = 1729
12X12X12 + 1X1X1 = 1729
There are no other numbers smaller than this which is the sum of 2 cubes.
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Wednesday, June 13, 2007
The number 1729 (called Hardy Ramanujam number)
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2 comments:
how is 1729 the smallest number by adding two cubes? the sum of cubes of 2 and 3 is 8+27 = 35. Am I missing something here?
It is the smallest number that is the sum of 2 cubes, and for 2 such different sets, that is,
10X10X10 + 9X9X9 = 1729
12X12X12 + 1X1X1 = 1729
35 is the sum of only one set, not 2 different sets
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