closed curvewith one cusp.
geometry, the cardioid is an epicycloidwith one cusp.
epicycloidproduced as the path (or locus) of a point on the circumference of a circleas that circle rolls around another fixed circle with the same radius.
limaçonwith one cusp. The cusp is formed when the ratioof a to b in the equationis equal to one.
inverse curveof a parabola[ [http://mathworld.wolfram.com/InverseCurve.html Weisstein, Eric W. "Inverse Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseCurve.html ] ] with focus as an invesion center [ [http://mathworld.wolfram.com/ParabolaInverseCurve.html Weisstein, Eric W. "Parabola Inverse Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ParabolaInverseCurve.html ] ] .
* an image of
circleunder complex map. [ [http://virtualmathmuseum.org/ConformalMaps/square2/index.html 3D-XplorMath Conformal Maps a*z^b+b*z ] ]
The name comes from the
heart shapeof the curve (Greek "kardioeides" = "kardia":heart + "eidos":shape). Compared to the heart symbol (♥), though, a cardioid only has one sharp point (or cusp). It is rather shaped more like the outline of the cross section of a plum.
Since the cardioid is an
epicycloidwith one cusp, in cartesian coordinatesit has parametric equations
where r is the radius of the circles which generate the curve, and the fixed circle is centered at the origin. The cuspis at (r,0).
The polar equation
yields a cardioid with the same shape. It is the same curve as the cardioid given above, shifted to the left r units, sothe cusp is at the origin.
For a proof, see
:"Four graphs of cardioids oriented in the four
cardinal directions, with their respective polar equations."
The area of a cardioid with polar equation:is:.
There are many cardioids in Mandelbrot set  :
* boundary of large central figure ( period 1 hyperbolic component) is a cardioid with equation :
* second largest cardioid is boundary of period 3 component on main antennae,
* generealy every mini copy of Mandelbrot set contains one cardioid.
Caustics can take the shape of cardioids. The caustic seen at the bottom of a coffee cup, for instance, may be a cardioid. The specific curve depends on the angle the light source makes relative to the bottom of the cup. The shape can be a
nephroid, which looks quite similar.
microphone- for a discussion of cardioid microphones
Radio direction finder
Radio direction finding
* [http://www.cut-the-knot.org/ctk/Cardi.shtml Hearty Munching on Cardioids] at
* Xah Lee, " [http://www.xahlee.org/SpecialPlaneCurves_dir/Cardioid_dir/cardioid.html Cardioid] " (1998) "(This site provides a number of alternative constructions)".
* Jan Wassenaar, " [http://www.2dcurves.com/roulette/rouletteca.html Cardioid] ", (2005)
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Look at other dictionaries:
Cardioid — Car di*oid, n. [Gr. kardio eidh s heart shaped; kardi a heart + e i^dos shape.] (Math.) An algebraic curve, so called from its resemblance to a heart. [1913 Webster] … The Collaborative International Dictionary of English
cardioid — [kär′dē oid΄] n. [Gr kardioeidēs, heart shaped < kardia, HEART + oeidēs, OID] Math. a curve more or less in the shape of a heart, traced by a point on the circumference of a circle that rolls around the circumference of another equal circle … English World dictionary
cardioid — noun 1》 Mathematics a heart shaped curve traced by a point on the circumference of a circle as it rolls around another identical circle. 2》 a directional microphone with a pattern of sensitivity of this shape. adjective of the shape of a cardioid … English new terms dictionary
cardioid — noun Date: 1753 a heart shaped curve that is traced by a point on the circumference of a circle rolling completely around an equal fixed circle and has an equation in one of the forms ρ = a(1 ± cos θ) or ρ = a(1 ± sin θ) in polar coordinates … New Collegiate Dictionary
cardioid — heart shaped … Dictionary of ichthyology
cardioid — /kahr dee oyd /, n. Math. a somewhat heart shaped curve, being the path of a point on a circle that rolls externally, without slipping, on another equal circle. Equation: r = a (1 cosA). [1745 55; < Gk kardioeidés heart shaped. See CARDI , OID] * … Universalium
cardioid — 1. noun An epicycloid with exactly one cusp; the plane curve with polar equation having a shape supposedly heart shaped 2. adjective Having this characteristic shape … Wiktionary
cardioid — Resembling a heart. [cardi + G. eidos, resemblance] * * * car·di·oid (kahrґde oid) heartlike; resembling a heart … Medical dictionary
cardioid — heart shaped Shapes and Resemblance … Phrontistery dictionary
cardioid — n. heart shaped geometrical figure (Mathematics) … English contemporary dictionary