Tuesday, July 6, 2010


So after my work on the square of a number, I tried to move up in the same direction, this time to look out for similarities in the cube of a number. This particular observation is a lot different from the one that I mentioned in the square of a number, in the sense that it establishes a link after a calculation has been carried out.

So, let us consider the following before we set off with the calculations:
N= Number, the cube of which needs to be determined.
N-1= Number that precedes N.
Now, (N-1)cubed gives the cube of the number (N-1)

So the cube of the number N can be derived from the cube of the number (N-1) in the following way:
Ncubed = (N-1)cubed + 3{N*(N-1)} + 1 Eq (i)

Now, in order to illustrate the above linkage further, let me take two random consecutive numbers 5&6.
N = 6
N-1 = 5

Now cube of 5 is (N-1)cubed = 125

So, the cube of 6 according to the above mentioned observation should then come down to:
6cubed = 5cubed + 3{6*5} + 1
6cubed = 125 + 90 + 1
6cubed = 216.

This observation holds true for the calculation of the cube of a number from the cube of the number that precedes it. However, I would not recommend using this observation as this involves a multiplication, which can prove to be cumbersome in case the numbers turn out to be large. But in any case, this analogy again gives us the link that exists between the numbers and their further calculations, just as it did in case of the squares.

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