The Sagrada Familia Magic Square

Sagrada Familia

The Temple Expiatori de la Sagrada Família ("Expiatory Temple of the Holy Family"), often simply called the Sagrada Família, funded by private donations, is a massive Roman Catholic church under construction in Barcelona, Spain. Construction began in 1882 and continues to this day. La Sagrada Familia, Gaudi's most famous work, his masterpiece, is a monumental church dedicated to the Holy Family. The Cathedral, one of the most popular attractions in Spain, is a synthesis of his architectural knowledge with the complex system of symbolism and a visual explication of the mysteries of faith. There would be extraordinary façades representing the birth, death and resurrection of Christ with eighteen towers symbolizing the twelve Apostles, the four Evangelists, the Virgin Mary and the Christ. The whole of the building is an allegory of the Christian religion. The 170 height meters arrow will incarnate Christ. The towers are decorated with words such as "Hosanna", "Excelsis", and "Sanctus".

Façade of Sagrada Família

Antoni Gaudí, 1910

The Spanish architect Antoni Gaudí (1852-1926); proposed that the Sagrada Família cathedral would take 200 years to complete. He devoted 43 years of his life to it before being killed by a streetcar (aged 74; 74   ⇒   7 + 4 = 11 = 33/3 = 1/3 of the Sagrada Square's magic constant, 33 here below). He was buried in the midst of La Sagrada Família. As of 2007, the building works are expected to be completed around 2026, the 100th anniversary of Gaudi's death. It has no roof so far, but there is a saying in Barcelona: "The only worthy roof for the Sagrada Familia is the sky".

Direction of works:

After a fire in 1936 that damaged the crypt and Gaudi's workshop, work on the façade of the passion restarted in 1952, based on the few original plans and models that survived the fire, and the four spires were completed between 1954 and 1976. In 1987 Catalan sculptor Josep María Subirachs joined the project, adding his controversial sculptures. Behind these figures is a magic square that appears to be his own design. Independent and with a strong personality, the artist decided to reside in the cathedral, since Subirachs needs to live where he develops his job. He regards it as his own life. Therefore, living inside his work of art allows him to work full-time.

Sculptor Josep María Subirachs

Façade of Sagrada Família

Sagrada Familia Magic Square

In squares of order 4 where the numbers run sequentially from 1-16 the magic constant (the sum of a single line, row or diagonal) is 34, but Subirachs' square does not contain the numbers 12 or 16 (see image, above). Instead, 10 and 14 are included twice, making a magic constant of 33, the age of Jesus Christ at the crucifixion.

Subirachs' square

Applet by

Subirach's cryptogram mounted on the facade. It is a magic square with all rows and columns adding to 33. In fact, there are dozens of regular symmetric combinations of 4 squares which add to 33.

Lee Sallows (July 12, 2001) points out that magic squares with a magic sum of 33 may be constructed without using duplicate integers.
Here is one (of several he provided) that uses the integers 0 to 16, but without the 4.