Geometry

“I am a geometrician, meaning I synthesise.” A. Gaudí

In full knowledge of the fact that he would not see the temple finished, Gaudí decided to plan the construction of the Sagrada Familia in modules, starting with the apse and the Nativity facade, knowing that if he managed to leave one of them finished, it would be more difficult to abandon construction.

In his desire to overcome the defects he saw in Gothic structural systems, Gaudí aimed to create a new architecture with balanced and self-supporting structures. In his workshop he experimented with and refined the constructional solutions he used on the building by using models. This way of working has been used by all his successors and is still practiced in the temple’s technical office. The Sagrada Familia was and still is a constructional challenge: it is one of the largest testing grounds for construction methods in the world.

Gaudí took his inspiration from two sources; the Christian message and nature. One was derived directly from the Holy Scriptures, tradition and liturgy. The other came from the observation of the natural world, providing him with a conceptual and methodological framework. Gaudí did not copy nature but analysed the function of its elements to formulate structural and formal designs which he then applied to architecture.

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Perhaps Gaudí saw that he had to find a clear and unequivocal manner to point the way forward for the construction work that he would leave unfinished. The architect planned many parts of the temple to be built combining geometric forms chosen for their formal, structural, lighting, acoustic and constructional qualities. The majority of the surfaces are ruled surfaces, making their construction easier.

The main contributions Gaudí made to architecture that can be seen in the Sagrada Familia are:

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Hyperboloids

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They can be solid as in the junctions between the columns and the vaulting, or hollow to allow light, symbol of God for Gaudí, to enter the temple. They can be found in the openings of the windows and the vaults.

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Paraboloids

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Gaudí used paraboloids to create linking surfaces between the vaults and the roofing and the columns on the Passion facade, as well as larger elements such as the towers and the sacristies. For him they represented the Holy Trinity.

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Helicoids

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According to the iconography of Gaudí they represent the rising movement that links the earth with heaven. Here they can be seen in the spiral staircases.

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Ellipsoids

Gaudí generated the rounded capitals of the main columns from ellipsoids, where the columns subdivide into branches.

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Double-twisted columns

To achieve greater stability and a slender and more harmonious effect, Gaudí designed all the branching columns as double-twisted columns formed by two helicoidal columns. The base of each column has a cross-section that is a polygon or star which as it twists to the right and the left transforms into a circle higher up.

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Conoids

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The best examples of conoids at the Sagrada Familia are the walls and roofs of the schools building.

After the long and careful empirical study of inverted models hung with weights from chains or strings and of graphical calculations, Gaudí arrived at the revolutionary idea of leaning columns branching out like trees and of using the idea of a forest, not only as a space of magical lighting conducive to intimacy and meditation, but as an organised and hierarchical structure for the optimal support of a beautiful vault of leaves. Each tree splits into branches and supports part of the vaulting; when one tree falls, the whole forest does not collapse.

 

Proportions

As well as ruled surfaces, Gaudí developed a system of proportions to be applied to all the dimensions of all parts of the Sagrada Familia.

He repeatedly used simple ratios based on twelfths of the largest dimension, as in 1 to ½, 1 to ⅔, 1 to ¾… etc. to provide proportions for the width, length and height of every part of the temple. For example; dividing the total length of the temple (90 metres) by 12 gives us a module of 7.5 metres, which is used in the design of the floor plan and the heights of the Sagrada Familia.

Different measurements can be compared to better appreciate his use of numerical series, not only the general dimensions of the temple but also the diameters and heights of the columns, the diameters of the window openings and vaults, etc. For example; the total height of a column is always, in metres, double the number of points of the cross-sectional polygon of its base: a column with a 12-point star as its base is 24 metres high; a column with an 8-point star base is 16 metres high, etc.

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