page_title: Antoni Gaudí
section_title: Geometrical forms
hierarchical_section_title: Antoni Gaudí / Style / Quest for a new architectural language / Geometrical forms
caption_attribution_description: La Sagrada Família per fí té un interior acabat: és una meravella, el fruit del geni únic d'Antoni Gaudí. Falten les paraules per descriure-ho. ca.wikipedia.org/wiki/Temple_Expiatori_de_la_Sagrada_Fam%... ========================================================== This is the crossing and dome of the Sagrada Família basilica, Barcelona, Catalonia. The catalan basilica of La Sagrada Família (The Holy Family) is a major icon of Barcelona. After more than a century of construction, in 2011 the interior was finished and consecrated by the pope Benedict XVI. Work began in 1882 and is scheduled to be completed in 2026. en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia www.sagradafamilia.cat/sf-eng/index.php
context_page_description: Antoni Gaudí i Cornet was a Catalan architect known as the greatest exponent of Catalan Modernism. Gaudí's works have a highly individualized, one-of-a-kind style. Most are located in Barcelona, including his main work, the church of the Sagrada Família.
  Gaudí's work was influenced by his passions in life: architecture, nature, and religion. He considered every detail of his creations and integrated into his architecture such crafts as ceramics, stained glass, wrought ironwork forging and carpentry. He also introduced new techniques in the treatment of materials, such as trencadís which used waste ceramic pieces.
  Under the influence of neo-Gothic art and Oriental techniques, Gaudí became part of the Modernista movement which was reaching its peak in the late 19th and early 20th centuries. His work transcended mainstream Modernisme, culminating in an organic style inspired by natural forms. Gaudí rarely drew detailed plans of his works, instead preferring to create them as three-dimensional scale models and moulding the details as he conceived them.
  Gaudí's work enjoys global popularity and continuing admiration and study by architects.
context_section_description: This study of nature translated into his use of ruled geometrical forms such as the hyperbolic paraboloid, the hyperboloid, the helicoid and the cone, which reflect the forms Gaudí found in nature. Ruled surfaces are forms generated by a straight line known as the generatrix, as it moves over one or several lines known as directrices. Gaudí found abundant examples of them in nature, for instance in rushes, reeds and bones; he used to say that there is no better structure than the trunk of a tree or a human skeleton. These forms are at the same time functional and aesthetic, and Gaudí discovered how to adapt the language of nature to the structural forms of architecture. He used to equate the helicoid form to movement and the hyperboloid to light. Concerning ruled surfaces, he said:
  Paraboloids, hyperboloids and helicoids, constantly varying the incidence of the light, are rich in matrices themselves, which make ornamentation and even modelling unnecessary.
  Another element widely used by Gaudí was the catenary arch. He had studied geometry thoroughly when he was young, studying numerous articles about engineering, a field that praised the virtues of the catenary curve as a mechanical element, one which at that time, however, was used only in the construction of suspension bridges. Gaudí was the first to use this element in common architecture. Catenary arches in works like the Casa Milà, the Teresian College, the crypt of the Colònia Güell and the Sagrada Família allowed Gaudí to add an element of great strength to his structures, given that the catenary distributes the weight it regularly carries evenly, being affected only by self-canceling tangential forces.
  Gaudí evolved from plane to spatial geometry, to ruled geometry. These constructional forms are highly suited to the use of cheap materials such as brick. Gaudí frequently used brick laid with mortar in successive layers, as in the traditional Catalan vault, using the brick laid flat instead of on its side. This quest for new structural solutions culminated between 1910 and 1920, when he exploited his research and experience in his masterpiece, the Sagrada Família. Gaudí conceived the interior of the church as if it were a forest, with a set of tree-like columns divided into various branches to support a structure of intertwined hyperboloid vaults. He inclined the columns so they could better resist the perpendicular pressure on their section. He also gave them a double-turn helicoidal shape (right turn and left turn), as in the branches and trunks of trees. This created a structure that is now known as fractal. Together with a modulation of the space that divides it into small, independent and self-supporting modules, it creates a structure that perfectly supports the mechanical traction forces without need for buttresses, as required by the neo-Gothic style. Gaudí thus achieved a rational, structured and perfectly logical solution, creating at the same time a new architectural style that was original, simple, practical and aesthetic.
caption: The nave in the Sagrada Familia with a hyperboloid vault. Inspiration from nature is taken from a tree, as the pillar and branches symbolise trees rising up to the roof.
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