into any position. Then one would readily admit that such a cissoid can be used to correctly solve the Delian problem. As a pedal curve The pedal curve of a parabola with respect to its vertex is a cissoid of Diocles. The geometrical properties of pedal curves in general produce several alternate methods of constructing the cissoid. It is the envelopes of circles whose centers lie on a parabola and which pass through the vertex of the parabola. Also, if two congruent parabolas are set vertex-to-vertex and one is rolled along the other; the vertex of the rolling parabola will trace the cissoid. Inversion The cissoid of Diocles can also be defined as the inverse curve of a parabola with the center of inversion at the vertex. To see this, take the parabola to be x = y2, in polar coordinate or: The inverse curve is thus: which agrees with the polar equation of the cissoid above. References "Cissoid of Diocles" at Visual Dictionary Of Special Plane Curves "Cissoid of Diocles" at MacTutor's Famous Curves Index "Cissoid" on 2dcurves.com "Cissoïde de Dioclès ou Cissoïde Droite" at Encyclopédie des Formes Mathématiques Remarquables (in French) "The Cissoid" An elementary treatise on cubic and quartic curves Alfred Barnard Basset (1901) Cambridge pp. 85ff Algebraic curves Articles containing proofs Roulettes (curve)