On the number of intersection points of the contour of an amoeba with a line

In this note, we investigate the maximal number of intersection points of a line with the contour of a hypersurface amoeba in Rⁿ. We define the latter number to be the R-degree of the contour. We also investigate the R-degree of related sets such as the boundary of an amoeba and the amoeba of the real part of a hypersurface defined over R. For all these objects, we provide bounds for the respective R-degrees.