y = mx + c
x = at + b, y = ct +d
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|
In fact nobody attempted a general definition of a curve until Jordan in his Cours d'Analysein 1893.
The inverse of a straight line is a circle if the centre of inversion is not on the line.
The negative pedal of the straight line is a parabola if the pedal point is not on the line.
Since normals to a straight line never intersect and tangents coincide with the curve, evolutes, involutes and pedal curves are not too interesting.
Other Web site:
Jeff Miller (Why is the slope of a straight line called m?)
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