Calculate the area and perimeter (arc length) of a cardioid curve.
Parameters
Properties
Area (A)117.8097
Perimeter (L)40.0000
About this calculator
What is a Cardioid?
A cardioid is a heart-shaped plane curve traced by a point on the perimeter of a circle that is rolling around the circumference of a fixed circle of the same radius. It is a special case of the limaçon family.
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Pro Tips
The parameter 'a' determines the size of the cardioid.
The cusp of the cardioid is at the origin if the equation is in standard polar form.
It can be represented as an epicycloid with one cusp.
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Fun Facts
"The name comes from the Greek word 'kardia', meaning heart."
"Cardioids appear in the study of fractals, specifically the Mandelbrot set (the main bulb is a cardioid)."
"Microphone polar patterns are often described as 'cardioid' because they pick up sound primarily from the front, in a heart-shaped pattern."
