Let me tell a story about the number 1729,which is known by the name Ramanujan number.
When Ramanujan ,the famous Indian mathematician was travelling in a car with Prof Hardy,the English mathematician,they witnessed a vehicle with the number 1729 on it.When prof Hardy mentioned about the same being a silly number,Ramanujan said that it was not so.He mentioned that it was the smallest number which could be expressed as a sum of 2 cube numbers in 2 different ways,and also that in one case the cubes were of consecutive numbers.Prof Hardy was surprised when Ramanujan gave the details.1729 is the sum of 729(cube of 9) and 1000(cube of 10).also the sum of 1(cube of 1) and 1728(cube of 12)
Let me now pose a question .Considering what Ramanujan said we can find that the difference between the cube of 12(1728) and cube of.10(1000) which is 728 will also be the difference between the cube of 9(729) and cube of1(1)Can we deduce that 728 is the smallest such number?
When Ramanujan ,the famous Indian mathematician was travelling in a car with Prof Hardy,the English mathematician,they witnessed a vehicle with the number 1729 on it.When prof Hardy mentioned about the same being a silly number,Ramanujan said that it was not so.He mentioned that it was the smallest number which could be expressed as a sum of 2 cube numbers in 2 different ways,and also that in one case the cubes were of consecutive numbers.Prof Hardy was surprised when Ramanujan gave the details.1729 is the sum of 729(cube of 9) and 1000(cube of 10).also the sum of 1(cube of 1) and 1728(cube of 12)
Let me now pose a question .Considering what Ramanujan said we can find that the difference between the cube of 12(1728) and cube of.10(1000) which is 728 will also be the difference between the cube of 9(729) and cube of1(1)Can we deduce that 728 is the smallest such number?
No comments:
Post a Comment