An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characteriza...
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1577 |
| Online Access: | http://hdl.handle.net/20.500.11824/1577 https://doi.org/10.1016/j.jmaa.2023.127107 |
| Access Level: | Embargoed access |
| Keyword: | Isoptic curves Isochordal-viewed curves Curves of constant Φ-width Support function Hedgehogs Regular polygons |
| Summary: | A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs. |
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