Magic Square on the Sagrada Familia

In June, I was lucky enough to explore the beautiful city of Barcelona. It was an incredible few days walking the sunny streets, lying on the beach and gazing at the incredible buildings that make up the city. My favourite sight, however, was the Sagrada Familia. This beautiful basilica is credited to Antoni Gaudi, who took over the project in 1883 but unfortunately didn’t see it finished. Construction began in 1882 with the first stone being laid on 19th March and the work is still ongoing today. The 40 years Gaudi spent designing the cathedral was cut short when he died in a tram accident. As well as experiencing the beauty of the Sagrada Familia from the street below, tourists can also pay to enter the basilica witness even more of Gaudi’s architectural genius.

The building features a number of facades, including the nativity façade, which was completed whilst Gaudi was still alive. The passion façade is decorated by the works of Josep Maria Subirachs. Since the plans drawn up by Gaudi for the Sagrada Familia were destroyed after his death, other artists have been continuing his work. In this façade there is a lot of symbolism in the smallest of details. For example, in the magic square behind the scene of Judas’s kiss. [1]


What is a “magic square”?

Mathematicians have been interested in magic squares for thousands of years. They are grids of numbers which have the particular property that numbers in any row, column or main diagonal add up to the same number, namely the “Magic Constant”. The numbers have to be distinct, positive integers and each magic square has an order which is the number of rows or columns.

These squares are said to be magic because they have often been tied to the supernatural. 4000 years ago in China, a 3×3 magic square was given the name “lo shu” and was meant to have spiritual importance. The squares also have magical connotations in other parts of the world: Indian amulets with magic squares on them are worn for protections; Turkish warriors wore them on shirts and in western Europe they have been used by astrologers. [2]

So why use a magic square on the passion façade of the Sagrada Familia? Well, there are a number of theories as to the meanings behind this design most obviously, the Magic Constant 33 representing the years of Jesus’ life

Magic Square from Melancholia I

Magic Square from Melancholia I

It also has links to one of the first magic square seen in art (pictured to the left). It was depicted Melancholia I by Albrecht Dürer, engraved in 1514. This square has a magic constant of 34. This magic square has the additional properties of the quadrants and middle 4 numbers adding up to 34 as well as the lines.

By turning the square 180 degrees and reducing the numbers 16, 15, 12 and 11 by 1 you arrive at the square depicted on the Sagrada Familia. Although this explains the duplicates of numbers 10 and 14 and the missing numbers 16 and 11, it means that the square, is not actually a magic square. The numbers within the grid have to be distinct and the repetition breaks that rule. [3]

Mathematics within art is fascinating because there is meaning behind the numbers and it demonstrates the beauty of the subject to many non-mathematicians. Magic squares have occupied peoples time even when they didn’t realise it! Not only is Sudoku made of Latin Squares, a similar concept to magic squares, but Rubik’s Cubes can find origins in these squares too!




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