Difference between revisions of "Cardioid"
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|Image=CardioidEnvelope 400.gif | |Image=CardioidEnvelope 400.gif | ||
|ImageIntro=The Cardioid an [[epicycloid]] with one cusp. | |ImageIntro=The Cardioid an [[epicycloid]] with one cusp. | ||
− | |ImageDescElem=The | + | |ImageDescElem=The image is formed by tracing a point on the circumference of a circle of radius <math>a</math>, without slipping, on another stationery circle, as in the image below[[Image:cardioid 1.gif|left|thumb]]. |
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− | + | The curve is given by: | |
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+ | *Cartesian equation <math>({x^2} + {y^2} - 2ax)^2 = 4{a^2}({x^2} + {y^2})</math>, where <math>a</math> is the radius of the moving circle. | ||
+ | *Polar equation <math>r = a (1 - {\cos} {\theta})</math> | ||
+ | *Parametric equations | ||
+ | <math>x = a {\cos} t (1 - {\cos t})</math> | ||
+ | <math>y = a {\sin} t (1 - {\cos t})</math> | ||
+ | ==Properties== | ||
+ | *It has a cusp at the origin. | ||
+ | * | ||
|AuthorName=Wolfram Math World | |AuthorName=Wolfram Math World |
Revision as of 13:31, 2 June 2009
Cardioid |
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Cardioid
- The Cardioid an epicycloid with one cusp.
Basic Description
The image is formed by tracing a point on the circumference of a circle of radius , without slipping, on another stationery circle, as in the image below
.
A More Mathematical Explanation
The curve is given by:
- Cartesian equation , where '"`UNIQ--math-00 [...]
The curve is given by:
- Cartesian equation , where is the radius of the moving circle.
- Polar equation
- Parametric equations
Properties
- It has a cusp at the origin.
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.
[[Description::The Cardioid an epicycloid with one cusp.|]]