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Field: Geometry
Image Created By: The Math Book


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.

Cardioid 1.gif

A More Mathematical Explanation

Generating a Cardioid

When a is the radius of the moving circ [...]

Generating a Cardioid

When a is the radius of the moving circle, the Cardioid curve is given by:

  • Cartesian equation ({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2}).
  • Polar equation r = a (1 - {\cos} {\theta})
  • Parametric equation

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

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

Properties of Cardioids


Why It's Interesting

====Cardioid Microphone====

The cardioid microphone...

Cardioid's in the Mandelbrot Set

Show image

Fibonacci and Cardioids



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