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- figura geometrica (it)
- geometriai alakzat (hu)
- spezielle Rollkurve eines Kreispunktes auf einem Kreis gleichen Radius (de)
- плоская линия, которая описывается фиксированной точкой окружности, катящейся по неподвижной окружности с таким же радиусом (ru)
- courbe algébrique plane (fr)
- rovinná křivka (cs)
- tasokäyrä, jonka piirtää ympyrän kehälle laitettu piste kun ympyrä vierii samansäteisen ympyrän kehää pitkin (fi)
- typ krzywej płaskiej, odmiana epicykloidy (pl)
- type af kurve (da)
- type of curve (en)
- unukuspa epicikloido (eo)
- wiskundige planaire kromme (nl)
- Konkoidearen kasu berezia. Kurba sortzailea zirkulu bat da, puntu finkoa zirkuluan dago eta k konstantearen balioa zirkuluaren diametroa da. Hau da kardioidearen ekuazioa, koordenatu polarretan r = k (1 − cos θ). (eu)
- çemberlerin oluşturduğu kalp şeklindeki eğri (tr)
- curva produzida pelo caminho de um ponto em epicicloide (pt)
- نوعی خم (fa)
- 心臓に似た形をした平面曲線 (ja)
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- Cardioid (en)
- p/c020390 (en)
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- The envelope of the pencil of implicitly given curves with parameter consists of such points which are solutions of the non-linear system
which is the envelope condition. Note that means the partial derivative for parameter .
Let be the circle with midpoint and radius . Then has parametric representation . The pencil of circles with centers on containing point can be represented implicitly by
which is equivalent to
The second envelope condition is
One easily checks that the points of the cardioid with the parametric representation
fulfill the non-linear system above. The parameter is identical to the angle parameter of the cardioid. (en)
- The radius of curvature of a curve in polar coordinates with equation is
For the cardioid one gets (en)
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- The orthogonal trajectories of the pencil of cardioids with equations are the cardioids with equations (en)
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- Cardioid (en)
- Epicycloid--1-Cusped (en)
- Heart Curve (en)
- Proof for the radius of curvature (en)
- Proof of the arc length formula (en)
- Proof of the area formula (en)
- Proof with envelope condition (en)
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- Cardioid (en)
- Epicycloid1-Cusped (en)
- HeartCurve (en)
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- Cardioid (en)
- منحنى قلبي (ar)
- Cardioide (ca)
- Kardioide (de)
- Καρδιοειδής καμπύλη (el)
- Kardioida (cs)
- Kardioido (eo)
- Cardioide (es)
- Kardioide (eu)
- Cairdeoideach (ga)
- Cardioide (it)
- Cardioïde (fr)
- カージオイド (ja)
- 심장형 (ko)
- Kardioida (pl)
- Cardioïde (nl)
- Cardioide (pt)
- Кардіоїда (uk)
- Кардиоида (ru)
- 心脏线 (zh)
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