Abstract
The locus \(k_\alpha \) of all points where two different tangents of a planar curve k meet at a constant angle \(\alpha \) is called the isoptic curve of k. We shall look for curves k that coincide with their isoptic curves \(k_\alpha \) and call them autoisoptic curves. Describing a planar curve k by its support function d allows us to derive a system of two linear ordinary delay differential equations that have to be fulfilled by d in order to make k an autoisoptic curve. Examples of autoisoptic curves different from the only known examples, namely logarithmic spirals, shall be given. We do not provide the most general autoisoptic curves, since these involve ordinary delay differential equations with time dependent delays. We only treat the case of constant delays.
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Odehnal, B. (2019). Examples of Autoisoptic Curves. 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. https://doi.org/10.1007/978-3-319-95588-9_28
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DOI: https://doi.org/10.1007/978-3-319-95588-9_28
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