In a magic square of numbers, all rows, columns and diagonals have the same sum, or magic total. Here is an example:
1*5*9 8*3*4 6*7*2 (mt=15)
Here’s another:
06*07*11*10 15*02*14*03 04*13*01*16 09*12*08*05 (mt=34)
And another:
04*25*20*10*06 01*13*11*21*19 23*09*07*08*18 15*16*03*14*17 22*02*24*12*05 (mt=65)
And another:
35*15*10*18*11*22 05*25*33*12*07*29 34*30*04*14*21*08 02*16*27*17*23*26 03*24*09*19*36*20 32*01*28*31*13*06 (mt=111)
In all those magic squares, the magic total is fixed: the sum of all numbers from 1 to 36 is 666, so any individual line in a 6×6 magic square has to equal 666 / 6 or 111. In other kinds of magic figure, this rule doesn’t apply:
2*7*3 4***8 6*5*1 (mt=12)
6*3*4 2***8 5*7*1 (mt=13)
8*5*1 2***6 4*3*7 (mt=14)
8*1*6 4***2 3*5*7 (mt=15)
I call figures like that magic lattices. But the lattice is clearer in larger squares:
14*09*10*16*01 21****15****07 06*12*02*19*11 05****20****13 04*08*03*17*18 (mt=50)
08*06*13*16*15 18****01****11 10*12*20*07*09 05****03****19 17*02*21*14*04 (mt=58)
You can also use prime numbers, or numbers that are divisible only by themselves and 1. The prime 3×3 magic lattice can only have one magic total:
11*17*03 13****23 07*19*05 (mt=31)
But bigger squares can vary:
73*07*05*61*37 23****11****47 43*53*17*41*29 13****79****67 31*19*71*59*03 (mt=183)
37*29*47*17*59 67*61****05*03 19****41****73 53*71****07*11 13*23*31*79*43 (mt=189)
127*097*013*163*047*019*101 003*****109*****007*****037 139*149*067*041*071*011*089 083*****031*****179*****029 053*103*023*059*079*113*137 157*****151*****167*****043 005*061*173*073*017*107*131 (7x7, mt=567)
013*163*003*089*179*023*067 131*****107*****109*****173 053*103*037*061*047*157*079 059*****071*****007*****043 101*137*127*011*017*113*031 097*****151*****029*****139 083*073*041*019*149*167*005 (mt=537)
097*107*061*031*079*059*011 083*019*************101*053 041*****037*****007*****127 131*********137*********113 017*****013*****089*****071 003*103*************043*047 073*109*029*139*067*005*023 (mt=445)
31*16*09*56*25*54*19*48*23 65****38****36****42****27 34*62*63*11*53*15*08*02*33 21****50****04****35****61 01*59*24*07*26*52*22*32*58 57****17****44****05****43 06*47*49*39*13*18*46*51*12 29****28****60****64****14 37*55*03*45*20*30*40*41*10 (9x9, all integers, mt=281)
21*50*36*18*37*14*55*28*33 17****64****23****20****06 32*47*11*34*08*35*46*30*49 38****05****02****58****45 22*63*26*61*31*01*12*52*24 51****65****57****09****40 42*19*04*25*60*41*10*48*43 07****27****59****53****39 62*03*54*16*15*56*29*44*13 (all integers, mt=292)
127*173*023*137*073*197*007*103*061 131*************181*************101 047*************109*************019 031*************029*************191 199*043*017*041*179*193*059*013*157 167*************005*************037 003*************011*************107 113*************151*************089 083*149*079*053*163*067*071*097*139 (9x9, primes, mt=901)
043*139*109*137*013*053*193*023*029 181*157*********************163*079 101*****047*************149*****131 197*********019*****083*********071 007*************037*************127 113*********017*****191*********061 005*****151*************167*****031 089*107*********************067*199 003*173*059*041*103*073*179*097*011 (primes, mt=739)
089*193*127*007*079*003*181*101*109 173*149*********************107*139 059*****019*************103*****037 197*********017*****083*********131 043*************113*************167 071*********047*****157*********061 041*****013*************029*****011 053*151*********************179*097 163*199*005*191*031*067*073*023*137 (primes, mt=889)