The mathematical secrets and techniques hidden within the middle of the Sagrada Familia in Barcelona
In 2026 it’ll be 100 years because the dying of Antoni Gaudí, the architect of the Basilica of the Sagrada Familia in Barcelona. Whilst the wonderful thing about the temple is abnormal in itself, it turns into much more profound after we discover the numerical shapes hidden at the back of its placing paperwork.
Via considering the mathematical ideas that beef up its construction, the visible cohesion of the entire takes on a brand new size, giving it renewed capability, stability and coherence.
The mathematician Claudi Alsina i Català deeply studied the maths of the Sagrada Familia. He performed his first research on this box on the College of Barcelona and directed the doctoral thesis of Jordi Faulí, the architect these days answerable for the continuing works at the temple.
In his memoirs, Alsina said:
Many had questioned if the design of the Sagrada Familia contained any module or gadget of proportions that guided the metric relationships of the construction. (…) One Saturday afternoon, sitting at my table at house, with all of the knowledge and paperwork about this mysterious proportional gadget – if it existed – I found out it. The 7.5 meter module and the proportions between the divisors of 12 (1:4, 1:3, 1:2, 3:4, 2:3, 1) appeared to give an explanation for so much.
12: the magic quantity
It isn’t sudden that the quantity 12 performs a outstanding function within the construction of the church. Gaudí conceived the Sagrada Familia as a synthesis of structure and spiritual symbolism, and the quantity 12 seems regularly within the Bible: the 12 sons of Jacob, the 12 tribes of Israel, the 12 apostles and the crown of 12 stars within the Ebook of Revelation are only some examples.
However its which means isn’t simply symbolic. From a mathematical viewpoint, 12 is a host particularly appropriate for setting up proportions, because it has many divisors. Consistent with Alsina, the relationships between those dividers give an explanation for a big a part of the basilica’s proportional gadget.
The 7.5 meter module
In response to Alsina’s paintings, we invite you to take a short lived mathematical excursion of the Sagrada Familia.
The scale of the temple are according to the quantity 12 and a module of seven.5m. It’s 90 m lengthy (7.5 × 12) and 60 m large (7.5 × 8). The width of the principle nave is 45m (7.5×6).
When it comes to peak, the perfect vault is that of the apse, 75 m (7.5 × 10), adopted through the transept vault of 60 meters (7.5 × 8). The nave vault is 45 m top (7.5 × 6), the aisle 30 m (7.5 × 4) and the choir 15 m (7.5 × 2).
The Tower of Jesus Christ is the central and perfect tower of the cathedral. It has a peak of 172.5 meters (7.5 x 23), on the subject of the peak of the emblematic Montjuïc hill. It’s topped through a four-armed go 17 m top and 13.5 m large. Round it are the 4 evangelical spiers, which achieve a peak of 135 m (7.5 x 18).
The Celebrity of the Virgin Mary is situated on the most sensible of the tower of the similar identify. Canaan, CC BY
The Tower of the Virgin Mary, 138 meters top, is the second one tallest within the basilica. It’s topped through a 12-point superstar, which rests on 3 supporting hands. This superstar has a diameter of seven.5 m and is shaped through a normal dodecahedron, with pentagonal pyramid-shaped issues emerging on every face. Its reflections of sunlight and night time lighting fixtures give this superstar a novel good looks.
polyhedral towers
The polyhedra additionally occupy a outstanding position within the towers of the Sagrada Familia. The 4 towers of the Glory façade are crowned through dodecahedra, the 4 towers of the Nativity façade through abnormal truncated octahedrons, and the 4 towers of the Hobby façade through truncated cubes.
In every of the 12 towers a spire rises above those polyhedra. The ones devoted to the evangelists are topped with common icosahedrons that comprise spotlights that light up the nice go that sits on the most sensible of the Tower of Jesus Christ. Simply above every icosahedron is a sculpture that symbolically represents every evangelist. There are a large number of star-shaped polyhedra all the way through the church, particularly at the Nativity façade.
The towers of the Nativity façade, topped through octahedrons. Yura Tarasovskyy/Shutterstock A wooded area of towers
Catenary arches function prominently as key structural parts of the church, as they’re an excessively efficient means of moving quite a bit to the bottom with out the will for added beef up. They are able to be noticed within the gadget of susceptible columns that beef up the vaults of the internal naves, the vaults and ceilings themselves, and the façade of the Nativity.
Within the Sagrada Familia there are 4 various kinds of columns. They’re all double-helix torsion columns: every has a rounded star-shaped polygonal base and is shaped through the intersection of 2 reverse Solomonic columns. Above every one there’s a knot from which other branches emerge, very similar to the ones of a tree, which very successfully beef up the towers and the roof of the church.
The roof skylights also are single-leaf hyperboloids. Shaped through instantly traces, they’re simple to construct and optimize the seize and projection of sunshine.
The symbolism of seven and 33.
The church has different deeply symbolic hidden options. Take, for instance, the cover over the principle altar, which paperwork a normal heptagon 5 meters in diameter, the seven facets of which characterize the seven items of the Holy Spirit.
At the left, Depression I through Albrecht Dürer, with a numerical grid visual within the higher proper nook. At the proper, the magic sq. designed through the sculptor Josep Maria Subirachs. Jordi Domènech/Wikimedia Commons/, CC BY-SA
At the Hobby façade there’s a magic sq. during which the sum of all of the rows, columns and diagonals is 33. It sort of feels to be impressed through the magic sq. that looks within the engraving Depression I through Albrecht Dürer.
The maths that underpins the Sagrada Familia makes it much more gorgeous. Whilst the construction itself is a sight to behold, a deeper working out of the foundations at the back of it evokes even better admiration for the iconic genius of Antoni Gaudí.
