Search results
Results from the WOW.Com Content Network
A magic square in which the broken diagonals have the same sum as the rows, columns, and diagonals is called a pandiagonal magic square. [1] [2] Examples of broken diagonals from the number square in the image are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4. The fact that this square is a pandiagonal magic ...
A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant.
In a magic cube, a broken space diagonal is a sequence of cells of the cube that follows a line parallel to a space diagonal of the cube, and continues on the corresponding point of an opposite face whenever it reaches a face of the cube. [1] [2] The corresponding concept in two-dimensional magic squares is a broken diagonal.
The richer structure of geomagic squares is reflected in the existence of specimens showing a far greater degree of 'magic' than is possible with numerical types. Thus a panmagic square is one in which every diagonal, including the so-called broken diagonals, shares the same magic property as the rows and columns. However, it is easily shown ...
For the diagonal or pandiagonal classes, one or possibly 2 of the 6 oblique magic squares may be pandiagonal magic. All but 6 of the oblique squares are 'broken'. This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2-D square; broken oblique squares are 2-D in a 3-D cube.
Bimagic square; Broken diagonal; Broken space diagonal; C. Arthur Cayley; Conway's LUX method for magic squares; D. Diagonal magic cube; F. Frénicle standard form;
Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.
Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions. In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them ...