The mathematical secrets and techniques hidden on the center of Barcelona’s Sagrada Família
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 abnormal in its personal correct, it turns into much more profound once we discover the numerical paperwork that lie in the back of its putting paperwork.
By means of considering the mathematical ideas that underpin its construction, the visible team spirit of the entire takes on a brand new measurement, endowing it with a renewed capability, steadiness 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 lately in control of the temple’s ongoing building.
In his memoirs, Alsina said:
Many had questioned 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 the entire information and paperwork in this mysterious proportional machine – if certainly it existed – I came upon 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) appeared to give an explanation for a perfect deal.
12: the magic quantity
It isn’t surprising that the quantity 12 performs a outstanding function within the construction of the church. Gaudí conceived the Sagrada Família as a synthesis of structure and non secular 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 Guide of Revelation are only a few examples.
However its importance isn’t simply symbolic. From a mathematical standpoint, 12 is a host specifically well-suited to setting up proportions, because it has many divisors. In step 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 short lived mathematical excursion of the Sagrada Família.
The temple’s dimensions are in keeping with 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).
On the subject of peak, the very best vault is that of the apse, at 75m (7.5 × 10), adopted by way of the vault of the transept at 60 metres (7.5 × 8). The nave vault is 45m top (7.5 × 6), the aspect 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), with regards to the peak of the landmark hill of Montjuïc. It’s topped by way of a four-armed pass, 17m top and 13.5m extensive. Surrounding this are the 4 Evangelist Spires, which succeed in a peak 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 top Tower of the Virgin Mary is the second one tallest within the basilica. It’s topped by way of a 12-pointed superstar, which rests on 3 supporting hands. This superstar has a diameter of seven.5m, and is made up of a standard 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 by way of dodecahedrons, the 4 towers of the Nativity façade by way of truncated abnormal octahedrons, and the 4 towers of the Hobby façade by way of 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 massive 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 all the way through the church, specifically at the Nativity façade.
The towers of the Nativity façade, topped by way of 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 approach to switch so much to the bottom with out the will for added give a boost to. They are able to be noticed within the machine of sloping columns that give a boost to the vaults of the inner naves, the vaults and ceilings themselves, and the Nativity façade.
Within the Sagrada Família, there are 4 several types of column. All are double-helix torsion columns – each and every has a rounded, star-shaped polygonal base, and is shaped by way of 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 give a boost to 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, for example, the cover above the top altar, which paperwork a standard heptagon 5 metres in diameter, whose seven facets symbolise the seven items of the Holy Spirit.
At the left, Melancholia I by way of Albrecht Dürer, with a numerical grid visble within the best right-hand nook. At the correct, the magic sq. designed by way of the sculptor Josep Maria Subirachs.
Jordi Domènech/Wikimedia Commons/, CC BY-SA
At the Hobby façade there’s a magic sq. wherein the sum of all rows, columns and diagonals is 33. Apparently to be impressed by way of the magic sq. featured within the engraving Melancholia I by way of Albrecht Dürer.
The math that underpins the Sagrada Família makes it the entire extra stunning. Whilst the development itself is a sight to behold, a deeper figuring out of the foundations in the back of it evokes even larger admiration for the long-lasting genius of Antoni Gaudí.
