Curves

Pursuit Curve

Description

If $A$ moves along a known curve then $P$ describes a pursuit curve if $P$ is always directed towards $A$ and $A$ and $P$ move with uniform velocities. These were considered in general by the French scientist Pierre Bouguer in 1732.

The case here is where $A$ is on a straight line and was studied by Arthur Bernhart.

Pierre Bouguer was a French scientist who was the first to attempt to measure the density of the Earth using the deflection of a plumb line due to the attraction of a mountain. He made measurements in Peru in 1740. A more successful use of this method by the astronomer Maskelyne placed the density between 4.5 and 5.

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