Abstract
Abstract. Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,…) those most frequently employed in architectural design are: – Euclidean Geometry – Projective Geometry – The non-Euclidean geometries. Entire architectural periods are linked to specific types of geometry. Euclidean geometry, for example, was the basis for architectural styles from Antiquity through to the Romanesque period. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture.
Highlights
For centuries geometry was effectively Euclidean Geometry: it was thought to be the one real geometry, representing space in a realistic way and, no other geometry was believed possible. (Stewart, 2016)
The general theory of relativity demonstrated that in the vicinity of bodies of great mass such as stars, space-time is not flat but, rather, curved. There is another type of geometry, called projective geometry, the development of which was based the perspective techniques used by painters and architects
Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry: in any case, throughout history the link between geometry and architecture has been strong
Summary
For centuries geometry was effectively Euclidean Geometry: it was thought to be the one real geometry, representing space in a realistic way and, no other geometry was believed possible. (Stewart, 2016). The general theory of relativity demonstrated that in the vicinity of bodies of great mass such as stars, space-time is not flat but, rather, curved. There is another type of geometry, called projective geometry, the development of which was based the perspective techniques used by painters and architects. If we are on a Euclidean plane between two parallel lines, we see that these meet on the horizon: the horizon is not part of the plane but is a "line at infinity" Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry: in any case, throughout history the link between geometry and architecture has been strong. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture
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