cardioid
Sign in to savethumb|A cardioidthumb|right|200px|The caustic (optics)|caustic appearing on the surface of this cup of coffee is a cardioid.
Article
28 sectionsContents
- Equations
- Proof for the parametric representation
- Metric properties
- Properties
- Chords through the cusp
- Proof of C1
- Proof for C2
- Cardioid as inverse curve of a parabola
- Cardioid as envelope of a pencil of circles
- Cardioid as envelope of a pencil of lines
- Proof
- ''Equation of the tangent'' of the ''cardioid'' with polar representation {{math|''r'' {{=}} 2(1 + {{thinsp|cos|{{varphi}}}})}}
- ''Equation of the chord'' of the ''circle'' with midpoint {{math|({{thinsp|1,|0}})}} and radius {{math|3}}
- Conclusion
- Cardioid as caustic of a circle
- Cardioid as pedal curve of a circle
- Proof
- The evolute of a cardioid
- Proof
- Orthogonal trajectories
- Proof
- In different positions
- In complex analysis
- Caustics
- See also
- Notes
- References
- External links
thumb|A cardioidthumb|right|200px|The caustic (optics)|caustic appearing on the surface of this cup of coffee is a cardioid.
In geometry, a cardioid () is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion. A cardioid can also be defined as the set of points of reflections of a fixed point on a circle through all tangents to the circle.