Special Polar Graph 1
Cardioid
A cardioid is a two-dimensional plane figure that has a heart-shaped curve. The word “cardioid” originated from a Greek word, which means “heart”. Hence, it is called a heart-shaped curve. The shape of a cardioid can be compared to the cross-section of an apple excluding its stalk.
It is a form of a sinusoidal spiral. This curve is the inverse of a parabola having focus at the centre of inversion. A cardioid does have exactly 3 parallel tangents with any particular gradient. It has a cusp (formed by the intersection of two branches of a curve). The length of the passing through the cusp of the cardioid is 4a, where “a” be the circle radius.
Polar Equation of Cardioid
The polar equation of the horizontal cardioid is given by:
The polar equation of the vertical cardioid is given by:
Parameters
- a is a constant that is a constant that determines the size of the cardioid.
- n is the number of quater cycles the curve is shifted.
- v is the upper limit of the parameter t, it represents the endpoint of the interval over which you want to trace or display the curve.
Type "Polar SG1" to find in phone app.
https://www.geogebra.org/3d/nc3zbjke