More about 1729.
Ofcourse any school kid can tell you that the "Ramanujan Number" 1729 is the smallest positive integer that can be written as the sum of the cubes of two numbers in two different ways.
1729 = 10^3 + 9^3 = 12^3 + 1^3
I learned few interesting stuff recently.
1+7+2+9 = 19 and 19 * 91= 1729
Consider the prime numbers 7,13 and 19 which form an arithmetic progression, 7*13*19 = 1729
1729 is not "really" the smallest number with the property that Ramanujan discovered, infact it is 91 if negative numbers are also considered.
91 = 4^3 + 3^3 = 6^3 + (-5)^3
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Of course....I was just about to say that! No seriously though who was Ramanujan? Was he that Indian mathematics genius who was taken to England and sadly died of a broken heart because he could not fit in? (at least that's the story I have in my memory)
ReplyDelete:-) It wasn't a broken heart that killed him, but tuberculosis. Ramanujan was to maths what Mozart was to music and Einstein was to Physics.
ReplyDeleteoh...I had a book about him once from the library. But, like many books I started reading but then did not get the time to finish it...I wish I had.
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