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The Magic Square of the Sagrada Familia – What’s Behind?

Today we are not going to talk specifically about the Sagrada Familia, but one of its more curious elements: the “magic square” located next to the sculture of Judas Kiss.

While appreciating the Passion façade and the majority of Subirachs’ sculptural work, more than once guests are amazed to find a progression of numbers inside a square and ponder what they can mean.

All things considered, it is an enchantment square, yet for this situation, it is an exceptionally extraordinary one. In this article, we’ll attempt to clarify why.

To ensure that everybody understands, a magic square is an arrangement of numbers (usually integers) in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number.

Magic Board at Sagrada Familia behind Judas Kiss
The sculpture of the Judas Kiss

In the Fagrada Familia we can find an example of magic square, located on the facade of the Passion and, despite what many people think, made by the sculptor Josep Maria Subirach not by the famous architect Antoni Gaudí.

The constant that is obtained by adding the 4 rows, 4 columns and 2 diagonals of this square is 33. But also the four numbers in the vertices of the square added 33, or equally the four middle numbers, and the same applies to a total of 310 possible combinations of four numbers taken from those 16. Thirty-three was, according to Christian tradition, the age when Christ was crucified.

The magic Board of Sagrada Familia
The magic square

An enchantment square is a progression of numbers on a square lattice, put with the goal that any line, section or corner to corner line dependably means a similar number. This total is known as the magic steady of the square.

Enchantment squares begin with 3×3 networks, as there’s no conceivable answer for a 2×2 framework and a 1×1 matrix doesn’t bode well.

Typically, this implies putting associating entire numbers into the framework: for a 3×3 matrix, the numbers from 1 to 9; for a 4×4 matrix, the numbers from 1 to 16. Beginning from these principles, the enchantment steady can’t be picked and relies upon the whole of the numbers utilized.

For instance, in a 3×3 magic square where the entirety of 1+2+3+4+5+6+7+8+9=45, each line, section and corner to corner line entireties 45/3 = 15; in a 4 x 4 magic square, where the aggregate of the considerable number of numbers from 1 to 16 is 136, the enchantment consistent is 136/4 = 34. Thus, for a 5×5 square, the steady is 65; for a 6×6, it’s 111; and for a 7×7, 175.

solution of the magic square
Here the solution of the magic square

The Sagrada Família enchantment square, nonetheless, is 4×4 and doesn’t meet these fundamental beginning conditions. From one perspective, it doesn’t have every one of the numbers from 1 to 16 (it is feeling the loss of the 12 and 16) and a few numbers are rehashed. Then again ―and in this lies the representative key―, the enchantment steady isn’t 34 however 33.

Subirachs took a current magic square, from German painter Albrecht Dürer’s etching Melencolia I, and adjusted it, rehashing the numbers 14 and 10 rather than 12 and 16, to make it signify 33, the age Jesus is generally accepted to have been executed. What’s more, we say customarily trusted on the grounds that, verifiably, this has never been affirmed 100%. By and by, the facts demonstrate that 33 is additionally an emblematic number, and not under any condition arbitrary, in view of the significance of the number 3 in the Christian world, as the image of the trinity.

Another curious thing of this element is that not only is sculpted on the facade of the Passion of the Sagrada Familia, but also in other 33 minor details of the interior: so, the square has a total of 310 combinations that add up to 33.

In fact, the 4×4 square, is much more complicated, with 110 possible solutions that, turned different ways, give us 880 variants. Dürer’s is one of these. They all have 34 as the magic steady, however we can see that a few arrangements are more supernatural than others as far as the quantity of conceivable blends that mean 34.

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