Arithmetic performs a task in the wonderful thing about the Sagrada Familia. From its proportions to its geometric shapes, Gaudí’s construction presentations how numbers can form structure this is immediately strong, resplendent and deeply symbolic.
The 12 months 2026 marks the centenary of the demise of Antonio Gaudi, the architect of the Sagrada Familia Basilica in Barcelona. If the wonderful thing about the construction is outstanding in itself, it good points even higher intensity once we uncover the mathematical paperwork that underlie its distinctive structure.
Through exploring the mathematical ideas that construction the entire, the visible unity of the monument acquires a brand new size, revealing an structure wherein capability, stability and coherence give a boost to every different.
Definitely, the one who has studied the math of the Sagrada Familia maximum deeply is Claudio Alsina and Catallo. Skilled in arithmetic on the College of Barcelona, he additionally supervised the PhD thesis of the website online’s present leader architect, Jordi Fauli.
In her memoirs, Alsina writes:
“Everybody puzzled if the design of the Sagrada Familia used to be according to a module and a gadget of proportions that guides the entire metric relationships of the construction. (…) One Saturday afternoon, sitting at my table at house, with the entire paperwork and the entire information associated with this mysterious gadget of proportions – did it in point of fact exist between metric and seven meters. -, I found out. it appeared that the divisors 12 (1:4, 1:3, 1:2, 3:4, 2:3, 1) they give an explanation for numerous issues.
Quantity 12, the central part
It’s not unexpected that the quantity 12 occupies a central position within the construction of the construction. Gaudí designed the Sagrada Familia as a synthesis between structure and spiritual symbolism, and 12 is ubiquitous within the Bible: the twelve sons of Jacob, the twelve tribes of Israel, the twelve apostles and even the crown of twelve stars from the Guide of Revelation are only a few examples.
However its pastime isn’t restricted to its symbolic importance. From a mathematical standpoint, 12 is a specifically excellent quantity for figuring out proportions as it has many divisors. It’s the relationships between those walls, in line with Alsina, that give an explanation for a big a part of the basilica’s gadget of proportions.
Given those foundations, each symbolic and mathematical, the relationship between structural components and the quantity 12 is subsequently no longer unexpected.
7.5 meter module
Development on Alsina’s paintings, we give you a brief seek advice from to the Sagrada Familia from a mathematical point of view. The size of the temple are carefully associated with the quantity 12 and the module of seven.5 meters. The duration of the construction is 90 meters (7.5×12), the width is 60 meters (7.5×8), whilst the width of the principle send reaches 45 meters (7.5×6).
The heights observe the similar theory: the easiest is the vault of the apse, with 75 meters (7.5 × 10), adopted by way of the vault of the transept, 60 meters top (7.5 × 8). Then observe the vault of the nave, at 45 meters (7.5 × 6), the vault of the facet aisles, at 30 meters (7.5 × 4), and after all the choir, whose top is 15 meters (7.5 × 2).
In step with Montjuic Hill
The Tower of Jesus is the central and easiest tower of the temple. At 172.5 m (7.5 × 23), its top mirrors that of Montjuic hill. On the best is a four-pointed move, 17 meters top and 13.5 meters large. 4 evangelist towers upward thrust round it, emerging to 135 m (7.5 × 18).
Sagrada Familia celebrity on best of Maria’s tower. From Canaan, CC BI
At 138 meters, Mary’s tower is the second one tallest within the basilica. On the best is a twelve-pointed celebrity resting on 3 supporting palms. With a diameter of seven.5 meters, this celebrity consists of a standard dodecahedron, every face of which is prolonged by way of a pentagonal level within the form of a pyramid. Sunlight reflections and midnight inside lighting fixtures give it a singular attractiveness.
Polyhedra on best of the towers
Polyhedra also are ubiquitous within the towers of the Sagrada Familia, as this find out about explains. The 4 towers of the Glory facade are crowned with dodecahedrons, the ones at the Christmas facade with truncated abnormal octahedrons, and the ones at the Interest facade with lower cubes.
The nativity facade towers, topped with octahedrons. Iura Tarasovskii/Shutterstock
On the best of every of the twelve towers rises a pinnacle above the polyhedron. The towers devoted to the evangelists are topped with a standard icosahedron (cast our bodies made up of twenty faces) with projectors illuminating the massive move that dominates the tower of Jesus. Immediately above every icosahedron is a sculpture that symbolically represents the corresponding evangelist. The temple additionally has a lot of celebrity polyhedra, particularly at the nativity facade.
Those aren’t columns, those are forests!
Chain arches shape one of the most major structural components of the temple. This form is especially efficient in shifting lots to the bottom with out the desire for different supporting components. They’re situated within the gadget of vulnerable columns that give a boost to the vaults of the interior naves, within the vaults and ceilings themselves, in addition to at the facade of the Nativity of Christ.
There are 4 kinds of columns throughout the Sagrada Familia. All are columns with a double spiral twist. Their polygonal base takes the form of a celeb with rounded contours and is the results of the intersection of 2 reverse Solomon’s pillars. Each and every is prolonged by way of a knot from which a number of branches emerge, very similar to the branches of a tree, which give a boost to the towers and roof of the temple with outstanding potency.
Skylights also are single-layered hyperboloids.) Since they’re composed of hetero traces, their development is more effective whilst optimizing gentle seize and diffusion.
The symbolism of 2 numbers: 7 and 33
“Melencolia I”, by way of Albrecht Dürer, the place we see the magic sq. within the higher proper nook. At the proper, the magic sq. designed by way of the sculptor Josep Maria Subirachs.
Different numbers hidden within the temple have robust symbolic importance. That is, as an example, the case with the cover above the principle altar, a standard heptagon with a diameter of five meters whose seven aspects constitute the seven presents of the Holy Spirit.
At the facade of the Interest there may be a magic sq. with all traces, columns and diagonals totaling 33, a host with obtrusive spiritual connotations. It kind of feels to were impressed by way of the magic sq. depicted in Albrecht Dürer’s engraving Depression I.
Finding the math in the back of the Sagrada Familia best provides to the construction’s attractiveness and the admiration that Antoni Gaudí’s genius conjures up.
