Dual curve: Difference between revisions

Properties of the original curve correspond to dual properties on the dual curve. In the Introduction image, the red curve has three singularities – a [[Crunode|node]] in the center, and two [[Cusp (singularity)|cusps]] at the lower right and lower left. The black curve has no singularities but has four distinguished points: the two top-most points correspond to the node (double point), as they both have the same tangent line, hence map to the same point in the dual curve, while the two [[inflection point|inflection points]] correspond to the cusps, since the tangent lines first go one way then the other (slope increasing, then decreasing).