In mathematics , a magic cube is that miraculous rectangle , in which is, numerous integers specify inside a n x n x n pattern these kinds of that this value of this numbers with each row, each column, each one pillar as well as four most important space diagonals is actually matched for you to just one number, the actual so-called miracle frequent from the cube, denoted M3(n). It might be revealed that whether a wonder cube features the actual numbers 1, 2, ., n3, then it's got magic frequent (sequence A027441 )
If, within addition, that quantities on every single fantastic wonder cube ; otherwise, it truly is called some sort of semiperfect magic cube . The number n is termed this order connected with the particular powerful cube. If the particular amounts with figures over a powerful cube's pandiagonal cube .
Alternate definitionIn recent years, a different distinction for any perfect miraculous cube has gradually come into use. It will be based upon the truth that a pandiagonal miraculous square includes traditionally happen to be calledperfect, because almost all feasible wrinkles quantity correctly. This is not really the situation when using the over description for any cube.
As in the case regarding secret squares, a bimagic cube has the additional property associated with left over a magic cube when all of the entries are squared, some sort of remains a miracle cube below both experditions involving squaring the actual entries and of cubing the entries. (Only not one but two of those will be known, as of 2005.) A stays a miracle cube when the word options are squared, cubed, or maybe increased to the final power.
Magic cubes according to D rer's plus Gaudi Magic squaresA magic cube is usually offering the particular constraint of an provided powerful square appearing on considered one of its faces Magic cube with the powerful square involving D rer , plus Magic cube using the wonder square of Gaudi
See alsoPerfect magic cube
Semiperfect magic cube
Magic tesseract
Magic hypercube
Magic cube class
Asymptotic magic hyper-tesseract
Nasik secret hypercube
John R. Hendricks
MathWorld: Magic Cube
Harvey Heinz: All regarding Magic Cubes
Marian Trenkler: Magic p-dimensional cubes
Marian Trenkler: An algorithm pertaining to building powerful cubes
Marian Trenkler: On item in addition to multiplicative magic cubes
Ali Skalli's wonder squares as well as miraculous cubes
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