Talk:Diabolic square

34

I've figured that the following add to 34:

• rows and columns (8)
• any two pairs of opposite corners of 3-by-3 squares (28) - includes the two diagonals, six broken diagonals and four 3-by-3 squares
• each of the 2-by-2 squares within it (9)
• the four corners of the whole square (1)
• a pair of adjacent numbers on the top row, plus the corresponding pair on the bottom, and similarly on the sides (6)

That makes 52. Time to try and find the other 34.... -- Smjg 12:30, 16 Jan 2004 (UTC)

Indeed, in any 4x4 magic square there are 86 34s - the difference is that here 52 of them are regular geometric forms, compared to 10 in general. -- Smjg 12:31, 13 May 2004 (UTC)

#T093

• Halló! Do you know when the "term" "diabolic square" was used first time? Gangleri | Th | T 13:25, 23 July 2005 (UTC)

A mathematical definition ?

• Halló! "a magic square in which the same sum can be found not only in rows, columns and diagonals, but in a variety of different regular and geometric configurations." Is this a mathematical definition? I think not.
• "mathworld:" "The term used by Hunter and Madachy (1975, p. 24) and Madachy (1979, p. 87) to refer to a panmagic square." – So what? – What would be if they would have called them "Salomonic squares"? Would this had changed somthing?
• Personaly I assume that both "diabolic square" and "satanic square" are manipulatory names and express fear or want to associate fear with them. It is like calling somthing in Wikipedia a "troll".
• Associating entities as "good", "bad", "taboo" is tipical to some cultures but not universal. Probably this does not have its place in "sience". Regards Gangleri | Th | T 15:52, 23 July 2005 (UTC)

Some sources imply that it's just a synonym for panmagic square, but others seem to imply that these additional conditions (2x2 and 3x3 squares, etc.) must be satisfied for a diabolic square. But the latter assumption has no obvious generalisation to squares of sizes other than 4x4. Incidentally, there are only three distinct (modulo rotation, reflection and moving a row/column to the other side) 4x4 panmagic squares, and all of them have these extra 34s, so for the 4x4 case the definitions are equivalent.

I guess we ought to merge the two pages. Unless anybody can find otherwise, we should probably have the pandiagonal condition as the definition, with the extra sums merely mentioned as incidentals of the 4x4 case. -- Smjg 14:26, 16 January 2006 (UTC)

I've read a few papers on magic squares in the mathematical literature (I was working on pandiagonal Latin squares), and from what I've seen, panmagic square, Diabolic magic square have meant the same thing (also called Nasik square, pandiagonal magic square, and Jaina(?) square). [unsigned]

"Diabolical" and "satanic" are just exciting names for squares that are so "magical" as to be "diabolic" (or "satanic"). No emotion is expressed by these names except excitement at their many properties. Enthusiasts of that sort of mathematical recreation have tendencies towards such names. They weren't intending to be scientific; they were having fun. (Incidentally, the mathematical research literature has very bad terminology; the pure mathematicians didn't seem to care what everyone else meant by "magic square".) Zaslav (talk) 01:56, 4 November 2010 (UTC)

72 another panmagic square?

Is the Magic Square shown in Magic square talk and on my user page also a panmagic or diabolic square? Marburg72 04:08, 19 September 2007 (UTC)