The Cissoid of Diocles is a notable mathematical curve from ancient Greek geometry, named after the Greek mathematician Diocles, who studied it around the 2nd century BCE. It is defined in the context of a specific geometrical construction involving a circle and lines, and it has applications in the creation of certain types of solutions for cubic equations.
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For , this algebraic curve can be constructed using a circle of radius centred at and its tangent line . On a ray from the origin, subtract the distance to its nonzero circle intersection from the distance to the line. The resulting radial distance is , for . Thus a parametric curve for it isEliminating gives the displayed cubic equation. It has a cusp at the origin, horizontal tangent direction there, and vertical asymptote . Its name honours Diocles.