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Handbook of the Mathematics of the Arts and Sciences pp 1–31Cite as

Projections of Knots and Links

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Abstract

This chapter presents an introduction to the archaeological and historical aspects of the use of projections of knots and links for decorative purposes. These projections of knots and links have been created by man on various artifacts, for at least some 4500 years. Apparently, the most prominent types of artifacts in most of the studied civilizations and cultures have been decorated with knots and links. Some examples are the Greek and Roman mosaics of the Roman world and various artifacts and art forms in the British Isles in the Anglo-Saxon era. The working hypothesis is that these knots and links are potential projections of real-life three-dimensional objects or at least that the intention of their creators was to present a feeling or sense in the beholder that the images were depictions of actual physical knots or links. The topological study of knots and links consider objects in \(\mathbb {E}^{3}\). However, these projections can in one way be seen as two-dimensional designs and could thus be studied with a geometrical approach in \(\mathbb {E}^{2}\) instead or at least to some extent. From the perspective of decorative art, this may in fact be sufficient and even perhaps more convenient.

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  1. Gothenburg, Sweden

    Alexander Åström

  2. Ucklum, Sweden

    Christoffer Åström

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  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, Montana, USA

    Bharath Sriraman

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Åström, A., Åström, C. (2018). Projections of Knots and Links. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_16-1

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