(x2 + 2+12ax + 9a2)2 = 4a(2x + 3a)3
x = a(2cos(t) + cos(2t)), y = a(2sin(t) - sin(2t))
Click below to see one of the Associated curves.
|Definitions of the Associated curves||Evolute|
|Involute 1||Involute 2|
|Inverse curve wrt origin||Inverse wrt another circle|
|Pedal curve wrt origin||Pedal wrt another point|
|Negative pedal curve wrt origin||Negative pedal wrt another point|
|Caustic wrt horizontal rays||Caustic curve wrt another point|
The length of the tangent to the tricuspoid, measured between the two points P, Q in which it cuts the curve again is constant and equal to 4a. If you draw tangents at P and Q they are at right angles.
The length of the curve is 16a and the area it encloses is 2πa2.
In the parametric form the cusps occur at t = 0 , 2π/3 and 4π/3. Notice the similarity between the parametric form of the tricuspoid and the parametric form of the cardioid.
The pedal of the tricuspoid, where the pedal point is the cusp, is a simple folium. The pedal, where the pedal point is the vertex, is a double folium. If the pedal point is on the inscribed equilateral triangle then the pedal is a trifolium.
The caustic of the tricuspoid, where the rays are parallel and in any direction, is an astroid.
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