* Magic cube with Dürer's square

 
Magic cube 4x4x4 composed with 12 magic squares, including the one of Dürer:
 

 The sum of the elements of each pillar gives the magic constant...

 

...as well as the sum of each line..
 

 

 

 ... and each column

 

 
Albrecht Dürer (1471-1528), was a German painter, printmaker and theorist. He is the creator of an engraving called Melancolia that includes among others, the following magic square:
 
 
The magic constant is 34. It is the sum of each row, each colomn and each diagonal.
 
By extending my method of magic squares to the construction of magic cubes, we can use the magic square of Dürer as one of the faces of a magic cube. The assembly by horizontal layers of the four magic squares below is a magic cube (you may download the Excel file at the bottom of this page):
 

 

 

Each magic square making up this cube, displays the sum of 34 on every row and every column.

The addition of the elements of each pillar of the cube (e.g. the upper left corners of the squares: 16 + 44 -51 +25), always produces the magic constant of 34.

Remarkably, the cube contains 64 different numbers, that is as many as the number of cells in the cube.

 

 

 

 

Dürer's magic square (upper face)

 

16

3

2

13

5

10

11

8

9

6

7

12

4

15

14

1

 

 

second level (under Dürer's square)

44

55

-26

-39

36

-17

22

-7

-35

-30

51

48

-11

26

-13

32

 

 

third level

-51

-14

27

72

24

75

-46

-19

76

23

-18

-47

-15

-50

71

28

 

fourth level (bottom side the cube)

25

-10

31

-12

-31

-34

47

52

-16

35

-6

21

56

43

-38

-27

Still using the same method, one can build magic cubes containing the magic square of Antoni Gaudi.
   
 
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Ali Skalli,
Oct 14, 2009, 9:11 AM
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