Difference between revisions of "Cardioid"
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'''Cardioid is the pedal of a circle with respect to a fixed point on the circle.''' | '''Cardioid is the pedal of a circle with respect to a fixed point on the circle.''' | ||
+ | [[Image:Cardioidpedal1.png]] | ||
'''Cardioid is the catacaustic of a circle with light source on the circle.''' | '''Cardioid is the catacaustic of a circle with light source on the circle.''' | ||
'''Cardioid is also the envelope of circles with centers on a fixed base circle C and each circle passing through a fixed point P on the base circle C.''' | '''Cardioid is also the envelope of circles with centers on a fixed base circle C and each circle passing through a fixed point P on the base circle C.''' | ||
+ | [[Image:Cardioidenvelope.png]] | ||
'''Cardioid is the inverse of parabola with respect to its focus.''' | '''Cardioid is the inverse of parabola with respect to its focus.''' | ||
+ | '''Cardioid is also the conchoid of a circle of radius r with respect to a fixed point on the circle, and offset 2 r.''' | ||
+ | [[Image:Cardioidconchoid1.png]] | ||
|AuthorName=The Math Book | |AuthorName=The Math Book |
Revision as of 12:52, 28 June 2010
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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.
Contents
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
Generating a Cardioid
When is the radius of the moving circ [...]Generating a Cardioid
When is the radius of the moving circle, the Cardioid curve is given by:
- Cartesian equation .
- Polar equation
- Parametric equation
Properties of Cardioids
The evolute of a cardioid is equal to itself.
Cardioid is the pedal of a circle with respect to a fixed point on the circle.
Cardioid is the catacaustic of a circle with light source on the circle.
Cardioid is also the envelope of circles with centers on a fixed base circle C and each circle passing through a fixed point P on the base circle C.
Cardioid is the inverse of parabola with respect to its focus.
Cardioid is also the conchoid of a circle of radius r with respect to a fixed point on the circle, and offset 2 r.
Why It's Interesting
====Cardioid Microphone====
The cardioid microphone...
Cardioid's in the Mandelbrot Set
Show image
Fibonacci and Cardioids
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Caustics
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Teaching Materials
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