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| {{refimprove|date=September 2012}}
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| [[File:Radiodrome-simple-y-bw.png|thumb|100px|right|Simple pursuit curve]]
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| [[Image:Radiodrome-params-colour.png|thumb|250px|right|Curves of pursuit with different parameters]]
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| A '''curve of pursuit''' is a [[curve]] constructed by analogy to having a [[point (geometry)|point]] or points representing pursuers and pursuees; the curve of pursuit is the curve traced by the pursuers.
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| With the paths of the pursuer and pursuee parameterized 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
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| :<math>L(t)=F(t)+xF^\prime(t). \, </math>
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| ==Multiple pursuers==
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| [[Image:Four point pursuit curve.gif|thumb|left|baseline|150px|animation|Curve of pursuit of [[vertex (geometry)|vertices]] of a square (the [[mice problem]] for n=4).]]
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| 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. An example of this is the [[mice problem]].
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| {{-}}
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| == See also ==
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| *[[Radiodrome]]
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| *[[Logarithmic spiral]]
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| *[[Tractrix]]
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| ==External links==
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| {{Commons|Curve of pursuit}}
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| *[http://mathworld.wolfram.com/PursuitCurve.html Mathworld], with a slightly narrower definition that |''L''′(''t'')| and |''F''′(''t'')| are constant
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| *[http://www-history.mcs.st-and.ac.uk/Curves/Pursuit.html MacTutor Pursuit curve]
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| {{Differential transforms of plane curves}}
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| [[Category:Curves]] | |
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| {{geometry-stub}}
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Latest revision as of 18:42, 17 November 2014
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