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Geometry of Stairs

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Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 809)


Stairs are important elements in architecture. After an introduction to the function, history and design rules of stairs, the studies of the geometry of stairs are in the focus of this research and educational project in architecture. The geometries of stairs can be related to their typologies and the resulted movements in space. Moving directions can be derived from the geometries of stairs. Of particular geometric interest are the various spiral staircases, single and multi-run or single and polycentric spiral staircases. With the help of their respective geometric concept of screwing different movements and fascinating geometric objects are the results. Finally, the kind of movements on stairs related to the inclination is the theme of the sinus stairs. The sinus stairs offer, with continuously changing step height and step depth according to the sine curve, smooth movement, as if walking onto a natural hill. A sinus staircase had been built by the students in a walk-in project in order to test the thesis. The stairs with their geometries had been analyzed by 3D-models, drawings and physical models.


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We would like to thank Prof. Joachim Wienbreyer, University of Applied Sciences in Regensburg for guiding us to special staircases in Regensburg and giving us an insight into the work, research materials and models, collected and created by Friedrich Mielke. The inventor of the sinus stairs, Laurin Werner Bäumler, provided us with his documents and material to the development of his ideas. Finally, I thank our students Benedikt Blumenröder, Yuliana Brehmer, Moritz Brucker, Marian Buchheiser, Sabrina Funk, Jana Gretz, Jonas Heuser, Sarah Lutgen, Emmanuel Niyodusenga, Ernst-Markus Rauska, Anna Specchio, Angelika Walz, and Philipp Weber for their committed work.

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Correspondence to Cornelie Leopold .

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Leopold, C. (2019). Geometry of Stairs. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95587-2

  • Online ISBN: 978-3-319-95588-9

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