In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a cochleoid is a
snail
A snail is, in loose terms, a shelled gastropod. The name is most often applied to land snails, terrestrial pulmonate gastropod molluscs. However, the common name ''snail'' is also used for most of the members of the molluscan class Gastro ...
-shaped curve similar to a
strophoid
In geometry, a strophoid is a curve generated from a given curve and points (the fixed point) and (the pole) as follows: Let be a variable line passing through and intersecting at . Now let and be the two points on whose distance from ...
which can be represented by the
polar equation
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the or ...
:
the
Cartesian equation
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
:
or the
parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric obj ...
s
:
The cochleoid is the
inverse curve
In inversive geometry, an inverse curve of a given curve is the result of applying an inverse operation to . Specifically, with respect to a fixed circle with center and radius the inverse of a point is the point for which lies on the ray ...
of
Hippias' quadratrix.
[ Heinrich Wieleitner: ''Spezielle Ebene Kurven''. Göschen, Leipzig, 1908, pp]
256-259
(German)
Notes
References
*
''Cochleoid''in the
Encyclopedia of Mathematics
The ''Encyclopedia of Mathematics'' (also ''EOM'' and formerly ''Encyclopaedia of Mathematics'') is a large reference work in mathematics.
Overview
The 2002 version contains more than 8,000 entries covering most areas of mathematics at a graduat ...
*Liliana Luca, Iulian Popescu
''A Special Spiral: The Cochleoid'' Fiabilitate si Durabilitate - Fiability & Durability no 1(7)/ 2011, Editura "Academica Brâncuşi" , Târgu Jiu,
*Roscoe Woods: ''The Cochlioid''. The American Mathematical Monthly, Vol. 31, No. 5 (May, 1924), pp. 222–227
JSTOR
*
Howard Eves
Howard Whitley Eves (10 January 1911, New Jersey – 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics.
Eves received his B.S. from the University of Virginia, an M.A. from Harvard Universi ...
: ''A Graphometer''. The Mathematics Teacher, Vol. 41, No. 7 (November 1948), pp. 311-313
JSTOR
External links
at 2dcurves.com
*
Plane curves
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