ANTONI GAUDI

GEOMETRY IN ARTITECTURE

 "We have given this academic title either to a fool or a genius. Time will show.“-Gaudi’s teacher. We will see,is he a fool or a genius ?

MODERNISME Modernisme  also known, in English,

as Catalan modernism, was a Catalan cultural

movement. The name is a catch-all for a variety of artistic and cultural symptoms, and is often understood as an equivalent to a number of 3 art movements, such as Symbolism, Decadence and Art Nouveau / Jugendstil, active from roughly 1888 to 1911. The modernisme movement was centred on the city of Barcelona, and its best-known in architecture was Antoni Gaudí.So we will talk about Antonı Gaudi’s life,masterpiece and important of Antoni Gaudi for Geometry.

ANTONI GAUDI (LIFE) Antoni Gaudí was born in 1852 in Reus. He was the youngest of five children, of

whom three survived to adulthood. Gaudí had a deep opinion for his native

land and great pride in his Mediterranean heritage. He believed Mediterranean people to be endowed with creativity, originality and a natural sense for art and design.

He designed lampposts for Plaçe Reial

Some photos from Plaçe Reial

From La Sagrada Familia

In 1883 Gaudí was put in charge of the recently

initiated project to build a basilica called La Sagrada Família.

CASA BATLLO

RELATİONSHİP BETWEEN OF THE GAUDİ’S STRUCTURE AND GEOMETRY

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.

Hyperboloid Helicoid ColumnsHyperbolic Paraboloid

Gaudí found a lot of examples in nature, for example 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.’’

Inside of Casa Mila

  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.

Another geometrical form used by Gaudí,was the catenary curve.

Gaudí evolved from plane to 

spatial geometry, to lined geometry. These constructional forms are highly suitable 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

When he was building the La Sagrada Familia, He

inclined the columns so they could better resist the vertical pressures on their section. He also gave them a double turn helicoid shape (right turn and left turn), as in the branches and trunks of trees. This created a structure that is now known as fractal.

Exapmle for Fractal

In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it can be represented by the equation.

This is an elliptic paraboloid which opens upward.

The hyperbolic paraboloid is a doubly ruled surface shaped like a saddle.

For example a elliptic paraboloid.

For example a hyperbolic paraboloid.

Hyperboloid structures are architectural structures designed with hyperboloid geometry.

Often these are tall structures

such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative effect as well as structural economy.

The helicoid, after the plane and the catenoid, is the third minimal surface to be known.Its name derives from it’s parallel to the helix: for every point on the helicoid there is a helix contained in the helicoid which passes through that point.

Helix on cordinate system Helicoid on cordinate system

Finally,Gaudí achieved perfectly logical

solution, creating at the same time a new architectural style that was original, simple, practical and aesthetic.

Rosary of MontserratEntrance gate of the Guell Pavilions

Gaudi’s unfinished project