conchoid

plural conchoids

1. geometryAny 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).

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

   5 more examples

   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.

   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.

   1982, J. Lee Kavanau, Curves and Symmetry, volume 1, page 3

   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.

   2007, James Stewart, Single Variable Calculus, volume 2, page 662

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

   2009, Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method, page 68

2. geographyA conchoidal fracture in rock.

   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.

   1948, Tennessee Valley Authority, “The Hiwassee Valley Projects”, in Technical Report, volume 2, number 5, page 359