A plane quartic curve consisting of two separate branches either side of and asymptotic to a central straight line (the asymptote), such that if a line is drawn from a fixed point (the pole) to intersect both branches, the part of the line falling between the two branches is of constant length and is exactly bisected by the asymptote.
- Such curves are represented by the general equation (x − a)2(x2 + y2) = b2x2, where a is the distance between the pole and the asymptote, and b is the constant length. The branch on the same side of the asymptote as the pole typically has a cusp or loop.
- Nicomedes is famous for his treatise On conchoid lines which contain his discovery of the curve known as the conchoid of Nicomedes.
- The ruler has a fixed distance marked on it and one mark is kept on a given line while the other traces the conchoid curve.
- Nicomedes, who was highly critical of Eratosthenes' mechanical solution, gave a construction which used the conchoid curve which he also used to solve the problem of trisection of an angle.
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