Regular polygons on isochordal-viewed hedgehogs
A curve $\alpha$ is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along $\alpha$ such that their tangents to the curve at these points form a constant angle. In this paper some properties of isochordal-viewed hedgehogs and Holditch curves are stud...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1478 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1478 https://doi.org/10.1007/s00010-022-00886-2 |
| Access Level: | acceso embargado |
| Palabra clave: | Isoptic curves Isochordal-viewed curves Holditch curves Curves of constant φ-width Hedgehogs Regular polygons |
| Sumario: | A curve $\alpha$ is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along $\alpha$ such that their tangents to the curve at these points form a constant angle. In this paper some properties of isochordal-viewed hedgehogs and Holditch curves are studied. It is proved that, under some conditions, the construction of some closed regular polygons whose vertices move smoothly along the curve $\alpha$ is possible. The property is illustrated with some examples. Moreover, Holditch curves of isochordal-viewed hedgehogs are considered and it is seen that they feature similar regular polygon properties although they are, in general, not parameterized by a support function. Finally, a recursive iteration of some Holditch curves for isochordal-viewed hedgehogs is shown to converge to the curve of polygon centers. |
|---|