2026 marks the one hundredth anniversary of the loss of life of Antoni Gaudí, the architect of the Sagrada Familia Basilica in Barcelona. Whilst the temple’s good looks is outstanding in itself, it turns into much more profound once we discover the numerical paperwork that lie at the back of its hanging paperwork.
Via making an allowance for the mathematical ideas underlying its construction, the visible solidarity of the entire acquires a brand new measurement, giving it renewed capability, steadiness and coherence.
Mathematician Claudio Alsina i Catallo studied the maths of the Sagrada Familia intensive. He started his preliminary research on this box on the College of Barcelona and supervised the doctoral thesis of Jordi Fauli, the architect lately accountable for the continued building of the temple.
In his memoirs, Alsina mentioned:
Many have questioned whether or not the design of the Sagrada Familia contained some module or machine of proportions that guided the metric relationships of the construction. (…) One Saturday afternoon, sitting at my table at house, with the entire information and paperwork about this mysterious proportional machine – if it in reality existed – I came upon 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 provide an explanation for so much.
12: the magic quantity
It isn’t surprising that the quantity 12 performs a distinguished position within the construction of the church. Gaudí envisioned the Sagrada Familia as a synthesis of structure and spiritual symbolism, and the quantity 12 is closely represented within the Bible: the 12 sons of Jacob, the 12 tribes of Israel, the 12 apostles and the crown of 12 stars within the E-book of Revelation are only a few examples.
However its significance isn’t just symbolic. From a mathematical standpoint, 12 is a in particular appropriate quantity for figuring out proportions, as it has many divisors. Consistent with Alsina, the family members between those divisors shape the main a part of the proportional machine of the basilica.
7.5 meter module
Drawing on Alcina’s paintings, we invite you to take a brief mathematical excursion of the Sagrada Familia.
The size of the temple are according to the quantity 12 and the module of seven.5m. It’s 90 meters lengthy (7.5 × 12) and 60 meters huge (7.5 × 8). The width of the primary nave is 45m (7.5×6).
In the case of peak, the easiest vault is the vault of the apse, at 75m (7.5×10), adopted by means of the vault of the transept at 60 meters (7.5×8). The vault of the nave is 45m prime (7.5×6), the facet nave 30m (7.5×4), and the choir 15m (7.5×2).
The Tower of Jesus Christ is the central and easiest cathedral. It’s situated at 172.5 meters (7.5 x 23), just about the peak of the well-known Montjuic hill. It’s topped with a four-pointed move, 17m prime and 13.5m huge. Round it are 4 evangelistic towers, which succeed in a peak of 135 m (7.5 x 18).
The famous person of the Virgin Mary sits on most sensible of the tower of the similar title. Canaan, CC BI
The tower of the Virgin Mary, 138 meters prime, is the second one tallest within the basilica. It’s topped with a 12-pointed famous person, which rests on 3 supporting palms. This famous person has a diameter of seven.5 m and is composed of an ordinary dodecahedron, with pentagonal pyramid-shaped issues emerging from each and every facet. Its reflections of sunlight and night time illumination give this famous person a novel good looks.
Polyhedral towers
Polyhedra also are distinguished within the Sagrada Familia towers. The 4 towers of the Glory facade are crowned by means of dodecahedrons, the 4 towers of the Nativity facade are truncated abnormal octahedrons, and the 4 towers of the Interest facade are truncated cubes.
On each and every of the 12 towers above those polyhedra rises a tower. The ones devoted to the Evangelists are topped with an ordinary icosahedron containing spotlights that light up the huge move that sits atop the Tower of Jesus Christ. Without delay above each and every icosahedron is a sculpture symbolically depicting each and every evangelist. There are a large number of famous person polyhedra right through the church, particularly at the facade of the Nativity of Christ.
The towers of the facade of the Nativity of Christ, topped with octahedrons. Yura Tarasovskii/Shutterstock Woodland tower
Chain arches function prominently as key structural components of the church, as they’re a extremely environment friendly means of moving quite a bit to the bottom with out the desire for added make stronger. They are able to be noticed within the machine of susceptible columns that make stronger the vaults of the interior naves, the vaults and ceilings themselves, and the facade of the Nativity of Christ.
There are 4 various kinds of columns within the Sagrada Familia. All are double helix torsion bars – each and every has a rounded polygonal star-shaped base and is shaped by means of the intersection of 2 opposing Solomon’s bars. Above each and every is a knot from which sprout more than a few branches, very similar to the ones of a tree, which very successfully make stronger the towers and roof of the church.
Skylights within the roof also are single-leaf hyperboloids. They consist of heterosexual traces, are simple to build and optimize mild seize and projection.
The symbolism of seven and 33
The church has different deeply symbolic hidden options. Take, as an example, the cover above the primary altar, which paperwork an ordinary heptagon with a diameter of five meters, whose seven facets characterize the seven presents of the Holy Spirit.
At the left, Melancholia I by means of Albrecht Dürer, with the numerical grid visual within the higher proper nook. At the proper, the magic sq. designed by means of the sculptor Josep Maria Subirachs. Jordi Domenech/Wikimedia Commons/, CC BI-SA
At the facade of the Interest there’s a magic sq. wherein the sum of the entire rows, columns and diagonals is 33. It kind of feels to had been impressed by means of the magic sq. proven in Albrecht Dürer’s engraving Despair I.
The math underlying the Sagrada Familia makes it much more stunning. Even if the construction itself is a sight to behold, a deeper figuring out of the rules at the back of it evokes even larger admiration for the long-lasting genius of Antoni Gaudí.
