Noun
Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and intersects a given curve, C, and the distance from p to the point of intersection with C is a specified constant (note that for nontrivial cases two such points p satisfy the criteria, and the resultant curve has two parts).
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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.
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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.
A conchoidal fracture in rock.
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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.
Noun
Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and intersects a given curve, C, and the distance from p to the point of intersection with C is a specified constant (note that for nontrivial cases two such points p satisfy the criteria, and the resultant curve has two parts).
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If you consider a point on a radius of the rolling curve in generating a cardioid that is not on its circumference, the result is a conchoid called the limaçon of Pascal.