Not a big deal, millions might have already guessed it or might be using it. Just found it useful to mentally calculate the square of the next number quickly, if you know the square of a basic 'check-point' number like 10, 15, 20, 25, 30 etc.
The standard formula I use for such a technique is:
sqr(n+k) = sqr(n) + sqr(k) + 2*k*n
For e.g.: sqr(29) = sqr(25+4) = 625 + 16 + 2*4*25 = 625 + 216 = 841
Thus the above sqr(n+k) method of finding squares is very useful for quick calculation of squares using the left shifts in even multiples to find the value of the nearest power of 2 and then adding 'k' to determine the desired whole square quickly for computer algorithms as well as human calculations.
For humans, it is easy to calculate with the nearest multiple of 10 or 5 as 'n' and 'k' as the extra required to achieve the number (like in the previous example). For computers, it will be quick to take the nearest power of 2 as 'n', as they can quickly calculate the square of that n by left shifting. I did write an 'C' implementation of such a "Threshold Whole Square" algorithm, which can be found here.
Shashank
PS: The ball in the picture is called a "Spherical Cube". Its made of 6 squares. Yes, they are squares, even though they don't look like one. :-)
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