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Conchoid vs Conchoidal - What's the difference?

conchoid | conchoidal |

As a noun conchoid

is (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).

As an adjective conchoidal is

(mathematics) of or pertaining to a conchoid; that may be defined as a conchoid.

conchoid

English

(wikipedia 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

    Related terms

    * conchoidal

    See also

    * cardioid * cissoid * * strophoid

    conchoidal

    English

    (Conchoidal fracture)

    Adjective

    (en adjective)
  • (mathematics) Of or pertaining to a conchoid; that may be defined as a conchoid.
  • * , 1976, D. T. Whiteside (editor), The Mathematical Papers of Isaac Newton , Volume 7: 1691-1695, page 621,
    • a conchoidal hyperbola with an oval at its convexity.
  • (mineralogy, of a fracture) Irregular, with planar, concentric curves, similar to those on a mussel shell.
  • * 1821 , Coal'', entry in Andrew Ure, ''A Dictionary of Chemistry on the Basis of Mr Nicholson's , unnumbered page,
    • It[pitch-coal] is distinguished by its splendent lustre and conchoidal fracture.
  • * 2005 , Chapter 19: Lithic Studies'', Herbert D. G. Maschner, Christopher Chippindale (editors), ''Handbook of Archaeological Methods , Volume 1, page 719,
    • Some flakes detached in a controlled manner have characteristics of conchoidal fracture.
  • * 2011 , Robert C Shaler, Crime Scene Forensics: A Scientific Method Approach , page 479,
    • On one side of the radial edge, the conchoidal fractures form right angles, that is, form a perpendicular with the edge.
  • * 2011 , David H. Krinsley, John C. Doornkamp, Atlas of Quartz Sand Surface Textures , page 10,
    • If grains derived from these rocks are unweathered after separation from the parent rock (a very rare occurrence), they may contain either conchoidal breakage patterns if grains are large, or upturned plates and flat upper and lower surfaces if small grains are considered.
  • (mineralogy, of a mineral ) That fractures with planar concentric curves (e.g., as flint, chert or obsidian).
  • * 1821 , Focus of Philosophy, Science and Art , Volume 1, Issues 1-4, page 74,
    • The customary transitions of pitchstone are, into Chalcedony, Chert, Semi-opal; also into a substance resembling conchoidal shining jasper, found in clay strata, entangled in trap, or volcanic rock; and lastly, into Trap.