Cissoid vs Conchoid - What's the difference?
cissoid | conchoid | see also |
(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
(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,
* 1982 , J. Lee Kavanau, Curves and Symmetry , Volume 1,
* 2007 , James Stewart, Single Variable Calculus , Volume 2,
* 2009 , Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method ,
(geology) A conchoidal fracture in rock.
* 1948 , Tennessee Valley Authority, The Hiwassee Valley Projects , Technical Report, Issue 5, Volume 2,
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
English
(wikipedia cissoid)Noun
(en noun)conchoid
English
(wikipedia conchoid)Noun
(en noun)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.
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.
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.
page 68,
- One of the best choices is the conchoid , according to Newton the simplest curve after the circle.
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.