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Journal for Geometry and Graphics 23 (2019), No. 2, 221--233
Copyright Heldermann Verlag 2019

Geometric Aspects of Scalalogy

Cornelie Leopold
Faculty of Architecture, Technische Universitšt, Pfaffenbergstr. 95, 67663 Kaiserslautern, Germany

Stairs are important elements in architecture and can be studied under various aspects. Fundamental rules for stairs had been fixed already by Vitruv, Alberti, Palladio, and Blondel. The German stair researcher F. Mielke played a significant role in the development of scalalogy, the science of stairs, in the late twentieth century. After an introduction to the function, history and design rules of stairs, the studies of geometric aspects of scalalogy are in the focus of this research and educational project in architecture. The geometric aspects of stairs can be related to their typologies and the resulted movements in space. Moving directions can be derived from the geometries of stairs. Spiral staircases in different variants, single and multi-run or single and polycentric, are of particular geometric interest. Finally, the kind of movements on stairs related to the inclination is the theme of the sinus stairs. They offer, with continuously changing step height and step depth according to the sine curve, smooth movements, as if walking onto a natural hill. The paper concludes with a description of a related students' project.

Keywords: Staircase, Architectural Geometry, scalalogy, movement in space.

MSC: 00A67; 51N05, 97M80

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