# Cardioid

Cardioid
Field: Geometry
Image Created By: The Math Book

Cardioid

A cardioid is a curve which resembles a heart. Its name is derived from Greek where kardia means heart and eidos means shape, though it is actually shaped more like the outline of the cross section of an apple.

# Basic Description

In geometry, a cardioid is the curve traced by a point on the circumference of a circle that rolls around the circumference of another equal circle.

# A More Mathematical Explanation

The curve is given by:

• Cartesian equation $({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2})$, where '"`UNIQ--math-00 [...]

The curve is given by:

• Cartesian equation $({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2})$, where $a$ is the radius of the moving circle.
• Polar equation $r = a (1 - {\cos} {\theta})$
• Parametric equation

$x = a {\cos} t (1 - {\cos t})$

$y = a {\sin} t (1 - {\cos t})$