The temple’s geometry: the essence that gives it shape and meaning

When describing the Sagrada Família, it is common to say, for example, that the exterior has three façades with four bell towers each, six lanterns and a total of eighteen towers stretching up towards the heavens, while the inside is filled with a forest of columns on a 7.5-m by 7.5-m grid. Because it is practically impossible to explain the Basilica without referring to the names, mathematics and geometry, just as we cannot overlook the relationship between all of this, which makes up the physical shape of the temple, and the symbolic content, which structures its soul, as well as the structural skeleton that holds it all up.

When we look at the temple façades, we see how Gaudí evolved from the Gothic style towards ruled geometry, which gives his work a surprisingly modern feel. So, the windows in the basement are very neo-Gothic in style, and this can be seen in their mouldings and their robustness. On top of these, the rose windows on the first level are organised, still, in a very neo-Gothic style, with a central oculus and a crown of circles surrounding it. The geometry used for these circular openings is much more modern, though: a series of hyperboloids with paraboloid seams. Finally, the windows on the upper level are organised in a much freer manner, with an elliptical rose window that strays from the traditional layout of this type of window.

Nevertheless, this path Gaudí set off on towards geometry isn’t only a formal research project to bring never-before-seen wealth and exuberance to the building, it is also the result of much deeper research. One example is how light spreads inside the temple after passing through these windows: the shapes help the light shine over the surfaces and create a magical world inside that moves the spirit and encourages introspection. However, the symbolic goal is the most important of all, bringing meaning to the whole temple. So, we’ll go over the symbolic essence of the three geometric shapes that make the layout of the temple possible.



In researching how sunlight would get into the temple, Gaudí decided it should come in not only through the façades but also the roof, a big innovation of our temple compared to any of the large cathedrals around the world. The architect found the hyperboloid to be the best shape to bring light in. Its two-sided trumpet shape, opening up on opposite sides, funnels the light in on one side and scatters it on the other. So, the light that enters the upper attics, above the temple naves, is funnelled via a series of hyperboloids into the inside, perforating the vaults where less weight is needed, furthest from the inclined supports of the temple. However, Gaudí did not want to lose the traditional symbol of the vault keystone, at the central point of each ceiling module, which he transformed into a light lamp in coloured glass.





The association that Gaudí draws between the hyperboloid and light isn’t an isolated case: in a very similar manner, he associates the geometric figure of the helicoid with movement. A helicoid is a surface made from a helix turning on an axis and the circular staircases are a clear example of this shape at the temple. The Solomonic columns, which are helicoidal, have a helix shape from the ground up to the capital, giving them a feeling of upward movement. There are fantastic examples of these on the Bugadera porch at Park Güell, among other works. At the temple, there is also an example of this type of column, the one separating the windows in the cloister, but the great discovery Gaudí made in his obstinate study of this type of column was the double-twist column.

This is a column created from the intersection of two Solomonic columns turning in opposite directions. They become ever so slightly thinner as they go up, beginning with a few arrises that multiply successively in number and, doubling the initial number in each section, run through all sorts of polygonal figures, with more and more sides, until they become a circle.





The final great association that Gaudí drew between geometry and meaning is the hyperbolic paraboloid. Paraboloids are quite common and, in fact, a saddle or a mountain pass are examples of this geometric shape.

The paraboloid can be generated with straight lines and is the ruled surface par excellence. The surface of a paraboloid can be obtained by sliding a ruler resting on two straight lines in a space. If the straight lines are parallel, we would make a plane. But when they aren’t, we get a paraboloid. And this is what made Gaudí associate the paraboloid with the Holy Trinity. He said that, if one straight line represents the Father and the other the Son, the Holy Spirit is the ruler that unites them and unites them forever.

So, we see how the geometry of Gaudí’s shapes not only organises the structure of the temple, giving the project a sense of modernity that is still surprising today, but also gives it meaning. Because in Gaudí’s work, geometry, structure and symbolism are inseparable.


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