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Cissoid vs Conchoid - What's the difference?

cissoid | conchoid | see also |

As nouns the difference between cissoid and conchoid

is that cissoid is any of a family of curves defined as the locus of a point, P, on a line from a given fixed point and intersecting two given curves, C1 and C2, where the distance along the line from C1 to P remains constant and equal to the distance from P to C2 while conchoid is 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).

cissoid

Noun

(en noun)
  • (geometry) Any of a family of curves defined as the locus of a point, P'', on a line from a given fixed point and intersecting two given curves, ''C''1 and ''C''2, where the distance along the line from ''C''1 to ''P'' remains constant and equal to the distance from ''P'' to ''C 2.
  • :The cissoid of a circle and a line is a conchoid
  • conchoid

    Noun

    (en noun)
  • (mathematics, geometry) 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).
  • :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, '', 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.
  • * 1982 , J. Lee Kavanau, Curves and Symmetry , Volume 1, page 3,
  • 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.
  • * 2007 , James Stewart, Single Variable Calculus , Volume 2, page 662,
  • 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.
  • * 2009 , Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method , page 68,
  • One of the best choices is the conchoid , according to Newton the simplest curve after the circle.
  • (geology) A conchoidal fracture in rock.
  • * 1948 , Tennessee Valley Authority, The Hiwassee Valley Projects , Technical Report, Issue 5, Volume 2, page 359,
  • 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.

    Usage notes

    The fixed point (P'') of the construction may be referred to as the focus of the conchoid ; it may also be defined as the origin (of a Cartesian coordinate system) or the pole (if polar coordinates are used), and potentially referred to accordingly. The curve ''C is an example of a directrix.

    Derived terms

    * conchoid of de Sluze (strictly a cissoid) * (not actually a conchoid) * conchoid of Nicomedes

    See also

    * cardioid * cissoid * * strophoid