r2 = a2θ
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|
For any given positive value of θ there are two corresponding values of r, one being the negative of the other. The resulting spiral will therefore be symmetrical about the line y = -x as can be seen from the curve displayed above.
The inverse of Fermat's Spiral, when the pole is taken as the centre of inversion, is the spiral r2 = a2/θ.
For technical reasons with the plotting routines, when evolutes, involutes, inverses and pedals are drawn only one of the two branches of the spiral are drawn.
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