Conchoid

The conchoid of a circle with respect to a point on the circle is a cardioid if the fixed distance is equal to the diameter of the circle.

The Conchoid of Nicomedes is the conchoid of a straight line with respect to a point not on the line.

1815, Charles Hutton, Pappus, entry in A Philosophical and Mathematical Dictionary, Volume 2, page 147, He next treats of the properties of the Conchoid, which Nicomedes invented for doubling the cube; applying it to the solution of certain problems concerning Inclinations, with the finding of two mean proportionals, and cubes in any proportion whatever.

The classical conchoid construction is a non-orthogonal polar-curvilinear construction in which equal distances along a line are marked off from its point of intersection with a curve for various positions of the line as it rotates about a point.

These curves are called conchoids of Nicomedes after the ancient Greek scholar Nicomedes. He called them conchoids because the shape of their outer branches resembles that of a conch shell or mussel shell.

One of the best choices is the conchoid, according to Newton the simplest curve after the circle.

Conchoids of sound rock, from a few feet to 20 or more feet in diameter, entirely surrounded by comparatively thin layers of weathered material, were frequently encountered, sometimes in adjacent series.