Given this square-spiral pattern of numbers:
7 6 5
8 1 4
9 2 3
10 11 12...
Is it possible to create a equation that will give me an X,Y coordinate, with 1 being 0,0, if I have a number (N)?
I figured out an algorithm (of sorts) using the knowledge that evens^2(from 2 up)+1 give a diagonal line upright and odds^2 (from 1 up)+0 give a diagonal line down and that the side length is sqrt(next corner>N [as defined above])-1. This is quite slow and inefficient, hence the hope for some sort of equation or simpler logic to find the coordinates.
Thanks in advanced , and I hope this is the appropriate area to post this question.