Hot! Magic Cube

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In mathematics , a magic cube is the actual miracle square , that will is, numerous integers arranged in a n times n back button n style this kind of that the sum of the your numbers on every single row, each column, each and every pillar plus the four main room diagonals can be add up to a particular number, your so-called miracle continual belonging to the cube, denoted M3(n). It can be shown this whether a magic cube involves the amounts 1, 2, ., n3, in that case it's got miraculous consistent (sequence A027441 )

If, within addition, the figures with every perfect powerful cube ; otherwise, it is labeled your semiperfect miracle cube . The quantity n is known as this obtain on the miracle cube. If that sums of volumes on the powerful cube's pandiagonal cube .

Alternate definition

In recent years, an various explanation for that perfect wonder cube has progressively enter into use. It is dependant on the belief that a pandiagonal wonder rectangular provides traditionally already been calledperfect, since just about all doable wrinkles payment correctly. This is just not true with the earlier mentioned definition for the cube.

As in the event connected with magic squares, some sort of bimagic cube features the extra building of remaining a new miraculous cube when all of the entries will be squared, your remains a new magic cube under both the operations associated with squaring the work plus associated with cubing the entries. (Only two of those are known, when regarding 2005.) A remains a new powerful cube if your work usually are squared, cubed, or brought up towards fourth power.

Magic cubes depending on D rer's plus Gaudi Magic squares

A magic cube could be constructed with the constraint of any given magic square showing on certainly one of it's fronts Magic cube with all the wonder sq . associated with D rer , and Magic cube when using the secret square involving Gaudi

See also

Perfect powerful cube

Semiperfect powerful cube

Magic tesseract

Magic hypercube

Magic cube class

Asymptotic wonder hyper-tesseract

Nasik wonder hypercube

John R. Hendricks

MathWorld: Magic Cube

Harvey Heinz: All in relation to Magic Cubes

Marian Trenkler: Magic p-dimensional cubes

Marian Trenkler: An protocol to create miraculous cubes

Marian Trenkler: On additive along with multiplicative miraculous cubes

Ali Skalli's magic squares and magic cubes

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