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Johannes Itten, along with Walter Gropius and others, was one of the most important founders of the Bauhaus in Weimar, and a teacher at the same time. Even if Itten was not a mathematician, he had a great interest in different geometric forms, and revealed a great mathematical intuition. Itten realized "by hand" the important Fire Tower, applying translations, reductions and rotations of cubes and of portions of cone. On the occasion of the Kunstfest Weimar 2019, the organizers of the events, which were specifically dedicated to Itten, invited us to describe in mathematical language the lithograph entitled Das Haus des Weissen Mannes (1921), in which the cube is again the "protagonist" of mathematical transformations. [ABSTRACT FROM AUTHOR]

Two very different cities (Berlin and Copenhagen), with two different stories and two different environments, have two different architectures, namely, the Reichstag building in Berlin and the Treetop Experience in Copenhagen, that are differentially designed. Two geometric shapes, an ellipsoid and a hyperboloid of one sheet, are used to interpret the different architectures. A common architectural element in both architectures is a spiral walkway that allows for the buildings' usability without barriers. In this work, the two observed objects are presented in their respective environment, history and purpose. The shapes are interpreted, which reveals their geometric aspects that are associated with the functional and emotional effects of their architectural forms. Parameterization is the main mathematical tool through which the characteristic shapes are studied and mathematically expressed, using Linear Algebra and the Parametric Geometry of surfaces that are ideally close to the studied architectural objects. Moreover, the free and open-source programming language ASYMPTOTE is used for their virtualization, the model's reliability is assessed, and the analysis of the model's behavior is presented. [ABSTRACT FROM AUTHOR]

Elena Marchetti reviews book Viewpoints-Mathematical Perspective and Fractal Geometry in Art by Marc Frantz and Annalisa Crannel [ABSTRACT FROM AUTHOR]

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