This yr, 2026, marks the centenary of the demise of Antonio Gaudi, the architect of the Sagrada Familia. The wonderful thing about this temple, already odd, turns into much more profound when the numerical calculations hidden in the back of its bureaucracy are published.
It’s as though the visible cohesion of the complicated took on a brand new size when taking a look on the mathematical ideas that strengthen its construction, offering it with capability, stability and coherence.
Surely, the one that has studied the maths of the Sagrada Familia maximum deeply is Claudio Alsina i Catallo, who finished his preliminary research on this area of expertise on the College of Barcelona and supervised the doctoral thesis of the present architect, director of works of the temple, Jordi Fauli.
In her memoirs, Alsina states:
Everybody puzzled if within the design of the Sagrada Familia temple there was once a module and a machine of proportions that guided the entire metric relationships of the paintings. (…) One Saturday afternoon, sitting at my table at house, with the entire information and paperwork about this mysterious proportional machine, if it existed…, I found out it. The 7.5 meter module and the ratios between the 12 dividers (1:4, 1:3, 1:2, 3:4, 2:3, 1) appear to give an explanation for so much.
Quantity 12, the central part
It’s not unexpected that the quantity 12 performs a outstanding position within the construction of the temple. Gaudí conceived the Sagrada Familia as a synthesis of structure and non secular symbolism, and 12 is a host with a powerful biblical presence: the 12 sons of Jacob, the 12 tribes of Israel, the 12 apostles or the crown of 12 stars from the Guide of Revelation are only some examples.
However her pastime isn’t just symbolic. From a mathematical viewpoint, 12 is a in particular appropriate quantity for figuring out proportions, because it has many divisors. In truth, the relationships between those divisors, consistent with Alsina, give an explanation for a lot of the basilica’s proportional machine.
With this symbolic and mathematical background, the relationship between the structural components of the temple and the quantity 12 will have to now not be unexpected.
7.5 meter module
According to Alsina’s phrases, we invite you to in brief seek advice from the Sagrada Familia with a mathematical viewpoint.
The size of the temple are associated with the quantity 12 and the module of seven.5 meters. Its duration is 90 m (7.5 x 12), width 60 meters (7.5 x 8), and the width of the principle send is 45 m (7.5 x 6).
When it comes to peak, the best possible is the vault of the apse, with 75 m (7.5 × 10); then the vault of the transept, with 60 m (7.5 × 8); 45 meters for the vault of the nave (7.5 × 6); 30 meters for the aspect aisle (7.5 × 4) and 15 meters for the choir (7.5 × 2).
In step with Montjuic Mountain
The Tower of Jesus is the central and best possible tower of the temple, measuring 172.5 m (7.5 x 23), consistent with the peak of Montjuic mountain. It’s topped with a four-pointed move 17 meters prime and 13.5 meters vast. Round it are 4 evangelist towers, which achieve a peak of 135 m (7.5 x 18).
The Megastar of the Holy Circle of relatives crowning the Tower of Mary. From Canaan., CC BI
Mary’s tower, 138 m, is the second one best possible within the basilica. It’s topped with a celeb with 12 issues, which rests on 3 supporting hands. This celebrity has a diameter of seven.5 m and is shaped through a normal dodecahedron, at the face of which pentagonal issues upward thrust within the form of a pyramid. Sunlight reflections and inner evening lights give this celebrity a novel good looks.
Polyhedra in towers
Polyhedra also are very provide within the towers of the Sagrada Familia. The 4 towers of the Glory facade culminate in dodecahedrons, the 4 towers of the Nativity facade culminate in truncated abnormal octahedrons, and the 4 towers of the Interest facade culminate in truncated cubes.
Within the 12 towers, the height rises above those polyhedra. The ones devoted to the Evangelists culminate in a normal icosahedron containing spotlights that remove darkness from the huge move that presides over the Tower of Jesus. Without delay above each and every icosahedron is a sculpture with a symbolic illustration of the evangelist. There are a lot of celebrity polyhedra within the temple, particularly at the facade of the Nativity of Christ.
The nativity facade towers, topped with octahedrons. Iura Tarasovskii/Shutterstock It is not columns, it is a wooded area!
However, catenary arches are provide within the temple as the principle structural components, as a result of they’re an overly environment friendly approach of moving the weight to the bottom with out the will for different supporting components. They’re built-in into the machine of prone columns that strengthen the vaults of the interior naves, into the vaults and ceilings themselves, in addition to into the facade of the Nativity of Christ.
Throughout the Sagrada Familia you’ll in finding 4 various kinds of columns. They all are known as double helix torsion bars, they’ve a polygonal base within the form of a rounded celebrity and are shaped through the intersection of 2 reverse Solomon’s bars. Above each and every is a knot from which more than a few branches emerge, very similar to the ones of a tree, which very successfully strengthen the towers and roof of the temple.
Roof skylights also are unmarried leaf hyperboloids. Since they’re composed of heterosexual strains, their building is lighter and optimizes the seize and projection of sunshine.
The symbolism of 2 numbers: 7 and 33
Different numbers hidden within the temple are deeply symbolic. As an example, the cover over the principle altar, which is a normal heptagon with a diameter of five meters, whose seven facets represent the seven presents of the Holy Spirit.
At the Interest Facade there’s a numerical sq. through which all rows, columns and diagonals upload as much as 33, with obtrusive non secular connotations. It kind of feels to had been impressed through the magic sq. that looks in Albrecht Dürer’s Depression.
Proper, Albrecht Dürer’s Melencolia I, the place a numerical grid can also be observed within the higher proper nook. At the left, the magic sq. designed through the sculptor Josep Maria Subirachs. Wikimedia Commons/jordi domenech, CC BI-SA
An perception into the maths in the back of the Sagrada Familia makes it much more stunning and conjures up higher admiration for the genius of Antoni Gaudi.
