Paper detail

The $f$-belos

The \emph{arbelos} is the shape bounded by three mutually tangent semicircles with collinear diameters. Recently, Sondow introduced the parabolic analog, the \emph{parbelos} and proved several properties of the parbelos similar to properties of the arbelos. In this paper we give one step further and generalize the situation considering the figure bounded by (quite) arbitrary similar curves, the \emph{$f$-belos}. We prove analog properties to those of the arbelos and parbelos and, moreover, we characterize the parbelos and the arbelos as the $f$-beloses satisfying certain conditions.