Cardioid

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Cardioid
Cardioidmainimage.jpg
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.

Cardioid 1.gif


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})




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