This curve is a trisectrix, and is sometimes called the limaçon trisectrix. When formula_18, the limaçon is a simple closed curve. However, the origin satisfies the Cartesian equation given above, so the graph of this equation has an acnode or isolated point. When formula_19, the area bounded by the curve is convex, and when formula_20, the curve has an indentation bounded by two inflection points. At formula_21, the point formula_22 is a point of 0 curvature. As formula_23 is decreased relative to formula_24, the indentation becomes more pronounced until, at formula_25, the curve becomes a cardioid, and the indentation becomes a cusp. For formula_26, the cusp expands to an inner loop, and the curve crosses itself at the origin. As formula_23 approaches 0, the loop fills up the outer curve and, in the limit, the limaçon becomes a circle traversed twice. The area enclosed by the limaçon formula_28 is (b^2 +