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.

中文翻译：

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凸体等视曲线的等周不等式

给定平面中的凸体，我们定义角度 $$\alpha $$ 的等光曲线，对于任意但固定的角度 $$\alpha ,$$ 为始终在角度 $$\ 下看到 K 的曲线alpha $$ 在本文中，我们证明了平面中任何凸体的周长与其同位素曲线之间的不等式。此外，我们还通过等光曲线的某些元素的恒常性证明了欧几里得圆盘的一些特征。