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: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.
The issue of city walkability is nowadays a theme in evidence. The chapter proposes a two-level reasoning. At the city level, the goal is to recognize the parts where actions aimed at improving walkability can be more effective. The second level is more detailed: lacking pedestrian paths' specific graphs, the urban space is modeled through a raster with 1x1 m. cells. Considering a series of criteria, an impedance has been assigned to each cell (i.e., the cost of travelling the cell on foot). This approach is applied to the city of Torino (Italy), but it is largely generalizable. To calculate this impedance, inter alia, the Torino geo-topographic database was used. The elaborations described in this chapter are seen as an aid to stakeholders to reason on city walkability and to compare different points of view in an explicit and articulated way.
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