Curve of pursuit

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Curves of pursuit with different parameters

A curve of pursuit is a curve constructed by analogy to having a point or points which represents pursuers and pursuees, and the curve of pursuit is the curve traced by the pursuers.

With the paths of the pursuer and pursuee parametrised in time, the pursuee is always on the pursuer's tangent. That is, given F(t) the pursuer (follower) and L(t) the pursuee (leader), there is for every t with F′(t) ≠ 0 an x such that

$L(t)=F(t)+xF^\prime(t).$

Typical drawings of curves of pursuit have each point acting as both pursuer and pursuee, inside a polygon, and having each pursuer pursue the adjacent point on the polygon.

The curve was highlighted in the season 3 premier of the American TV show Numb3rs.