Sum of Two Cubes
Date: 01/12/2002 at 07:35:59 From: Gemm Subject: Cube numbers Find the smallest number that can be expressed as the sum of two cube numbers in two different ways
Date: 01/12/2002 at 17:05:48 From: Doctor Paul Subject: Re: Cube numbers The answer is 1729. 1729 = 1^3 + 12^3 = 9^3 + 10^3 What is more interesting about this is a celebrated story that goes with it. The great Indian mathematician Srinivasa Ramanujan (1887-1920) was ill in the hospital when a friend (the great British mathematician Godfrey Hardy) came to visit him. Hardy was well acquainted with Ramunujan's interest in numbers, so he noted that the number of the taxi he took to get the the hospital was rather uninteresting. The taxi number was, of course, 1729, and Ramanujan, though ill, immediately noted that 1729 was in fact quite interesting since it was the smallest number that could be written as a sum of two cubes in two different ways. How he had discovered this is anyone's guess. Computers have since verified that his answer was correct. Ramanujan became famous for coming up with formulas like this one off the top of his head. I hope this helps. Please write back if you'd like to talk about this more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/
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