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To: alt.magick From: milmoe@symcom.math.uiuc.edu (Andrew Milmoe) Subj: Magick Squares Formula (0000.msqfmla.am) Date: unknown Quoting: |unknown |...Andrew, are you willing to check the magic squares I have against |a math text on them? (Magic squares, having specific mathematical rules, |can actually be checked for accuracy, unlike most other things in magic.) Just an off-the-cuff analysis: for an NxN magic square, there are N^2 consecutive integers (our variables) to fill the squares with, and there are 2N+2 equations to satisfy (N rows, N columns, and two diagonals that each add up to (N^4 + N^2)/2N ). If we were dealing with real numbers here and not just integers, I'd say that there are N^2-(2N+2) degrees of freedom (that's the number of variables that we can assign any value to and still be able to solve the equations). Since we're dealing with consecutive integers, we're a bit more constrained - there may be equations to describe the system and account for this that I haven't thought of yet. Anyway, for Saturn's 3x3 square, we have 9 consecutive integers to deal with, and 8 equations, yielding 1 degree of freedom - I feel that only reflects the fact that it's possible to rotate the square and still satisfy all the conditions (barring having the same magickal significance). As I said, I'll have to check on what sort of equation would express the constraint that we're dealing with consecutive integers, and see if it has any effect (barring a rotation of the square) on the solutions. Whew! Did you really need to hear all that? ;) Andrew Milmoe milmoe@symcom.math.uiuc.edu
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