Abstract
Given a convex body in the plane, we define the isoptic curve of angle \(\alpha \), for an arbitrary but fixed angle \(\alpha ,\) as the curve from which K is always seen under an angle \(\alpha \) In this article we prove an inequality between the perimeter of any convex body in the plane and its isotopic curve. Moreover, we also prove some characterizations of the Euclidean disc by means of the constancy of some elements of the isoptic curve.
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Jerónimo-Castro, J., Rojas-Tapia, M.A., Velasco-García, U. et al. An Isoperimetric Inequality for Isoptic Curves of Convex Bodies. Results Math 75, 134 (2020). https://doi.org/10.1007/s00025-020-01261-w
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DOI: https://doi.org/10.1007/s00025-020-01261-w