2026 marks 100 years for the reason that loss of life of Antoni Gaudí, the architect of the Basilica of the Sagrada Família in Barcelona. Whilst the temple’s attractiveness is unusual in its personal correct, it turns into much more profound once we discover the numerical bureaucracy that lie at the back of its placing bureaucracy.
Via considering the mathematical rules that underpin its construction, the visible solidarity of the entire takes on a brand new size, endowing it with a renewed capability, stability and coherence.
Mathematician Claudi Alsina i Català deeply studied the math of the Sagrada Família. He undertook his preliminary research on this box on the College of Barcelona, and supervised the doctoral thesis of Jordi Faulí, the architect these days in command of the temple’s ongoing development.
In his memoirs, Alsina said:
Many had puzzled whether or not the design of the Sagrada Família contained some module or machine of proportions that guided the development’s metric relationships. (…) One Saturday afternoon, sitting at my table at house, with all of the knowledge and paperwork in this mysterious proportional machine – if certainly it existed – I found out it. The 7.5-metre module and the ratios between the divisors of 12 (1:4, 1:3, 1:2, 3:4, 2:3, 1) gave the impression to provide an explanation for an excellent deal.
12: the magic quantity
It isn’t a surprise that the quantity 12 performs a distinguished function within the construction of the church. Gaudí conceived the Sagrada Família as a synthesis of structure and spiritual symbolism, and the quantity 12 options closely within the Bible: Jacob’s 12 sons, the 12 tribes of Israel, the 12 apostles and the crown of 12 stars within the E book of Revelation are only some examples.
However its importance isn’t simply symbolic. From a mathematical viewpoint, 12 is a bunch in particular well-suited to organising proportions, because it has many divisors. In keeping with Alsina, the relationships between those divisors account for far of the basilica’s proportional machine.
The 7.5-metre module
Drawing on Alsina’s paintings, we invite you to take a temporary mathematical excursion of the Sagrada Família.
The temple’s dimensions are in response to the quantity 12 and a module of seven.5m. It’s 90m lengthy (7.5 × 12) and 60m extensive (7.5 × 8). The width of the principle nave is 45m (7.5 × 6).
In relation to top, the best vault is that of the apse, at 75m (7.5 × 10), adopted via the vault of the transept at 60 metres (7.5 × 8). The nave vault is 45m prime (7.5 × 6), the facet aisle 30m (7.5 × 4), and the choir 15m (7.5 × 2).
The Tower of Jesus Christ is the central and tallest of the cathedral. It stands at 172.5 metres (7.5 x 23), as regards to the peak of the landmark hill of Montjuïc. It’s topped via a four-armed pass, 17m prime and 13.5m extensive. Surrounding this are the 4 Evangelist Spires, which achieve a top of 135m (7.5 x 18).
The Big name of the Virgin Mary sits atop the tower of the similar identify.
Canaan, CC BY
The 138-metre prime Tower of the Virgin Mary is the second one tallest within the basilica. It’s topped via a 12-pointed superstar, which rests on 3 supporting fingers. This superstar has a diameter of seven.5m, and is made up of a normal dodecahedron, with pyramid-shaped pentagonal issues emerging from each and every face. Its reflections of sunlight and night-time illumination lend this superstar a singular attractiveness.
Polyhedral towers
Polyhedrons additionally characteristic prominently within the towers of the Sagrada Família. The 4 towers of the Glory façade are crowned via dodecahedrons, the 4 towers of the Nativity façade via truncated abnormal octahedrons, and the 4 towers of the Pastime façade via truncated cubes.
On each and every of the 12 towers, a spire rises above those polyhedrons. The ones devoted to the evangelists are topped with common icosahedrons containing spotlights that light up the huge pass that sits atop the Tower of Jesus Christ. Simply above each and every icosahedron is a sculpture that symbolically depicts each and every evangelist. There are a large number of star-shaped polyhedrons during the church, in particular at the Nativity façade.
The towers of the Nativity façade, topped via octahedrons.
Yura Tarasovskyy/Shutterstock
A wooded area of towers
Catenary arches characteristic prominently as key structural components of the church, as they’re a extremely efficient option to switch so much to the bottom with out the will for extra make stronger. They are able to be noticed within the machine of sloping columns that make stronger the vaults of the internal naves, the vaults and ceilings themselves, and the Nativity façade.
Within the Sagrada Família, there are 4 various kinds of column. All are double-helix torsion columns – each and every has a rounded, star-shaped polygonal base, and is shaped via the intersection of 2 opposing Solomonic columns. Above each and every one is a knot from which other branches emerge, very similar to the ones of a tree, which very successfully make stronger the towers and the roof of the church.
The skylights within the roof also are one-sheet hyperboloids. Made up of hetero strains, they’re simple to build, and optimise the seize and projection of sunshine.
The symbolism of seven and 33
The church has different deeply symbolic hidden options. Take, as an example, the cover above the prime altar, which bureaucracy a normal heptagon 5 metres in diameter, whose seven aspects symbolise the seven items of the Holy Spirit.
At the left, Melancholia I via Albrecht Dürer, with a numerical grid visble within the most sensible right-hand nook. At the correct, the magic sq. designed via the sculptor Josep Maria Subirachs.
Jordi Domènech/Wikimedia Commons/, CC BY-SA
At the Pastime façade there’s a magic sq. by which the sum of all rows, columns and diagonals is 33. It sounds as if to be impressed via the magic sq. featured within the engraving Melancholia I via Albrecht Dürer.
The math that underpins the Sagrada Família makes it all of the extra stunning. Whilst the development itself is a sight to behold, a deeper figuring out of the foundations at the back of it conjures up even higher admiration for the long-lasting genius of Antoni Gaudí.
