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.
- ‘Dürer calls the curve ‘ein muschellini’ which means a conchoid, but since it is not a true conchoid we have called it Dürer's shell curve (muschellini = conchoid = shell).’
- ‘Nicomedes is famous for his treatise On conchoid lines which contain his discovery of the curve known as the conchoid of Nicomedes.’
- ‘The conchoid has x = b as an asymptote and the area between either branch and the asymptote is infinite.’
- ‘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.’
- ‘Pappus tells us about the conchoid of Nicomedes in his Mathematical collection.’
Early 18th century: from conch + -oid.