Two Architectures: Two Compared Geometries

Two very different cities (Berlin and Copenhagen), two stories and two different environments, two architectures (Reichstag building in Berlin and Treetop Experience in Copenhagen) differentially finalized. Two geometric shapes (ellipsoid and hyperboloid of one sheet) that interpret in their architectures, of which they are support, their differences. A common architectural element: a spiral walkway that allows usability, without barriers, in both architectures. In this work the two objects observed are presented: in their environment, in their history and in their purpose. The shapes are interpreted, revealing their geometric nature, and the geometric aspects are associated with the functional and emotional effects of the architectural forms. The main mathematical tool, through which the characterizing shapes are studied and mathematically expressed, is the parametrization, by the Linear Algebra and Parametric Geometry, of surfaces, that are ideally close to the studied architectural objects. Moreover their virtual realization, using the free and open-source programming language ASYMPTOTE, and, after having assessed the reliability, the analysis of model behavior are presented.