Straight Line

Cartesian equation:
y = mx + c
or parametrically:
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

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

The straight line must be one of the earliest curves studied, but Euclid in his Elementsalthough he devotes much study to the straight line, does not consider it a curve.

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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JOC/EFR/BS January 1997

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