# Curve of pursuit

A curve representing a solution of the "pursuit" problem, which is posed as follows: Let a point be moved uniformly along a given curve. The trajectory has to be found of the uniform movement of a point , such that the tangent drawn towards the trajectory at any moment of the movement would pass through the position of corresponding to that moment in time.

Figure: c027400a

In a plane, the system of equations which the curve of pursuit must satisfy takes the form

where is the slope of the curve of pursuit, and is the equation of the given curve.

The "pursuit" problem was posed by Leonardo da Vinci and solved by P. Bouguer (1732). For a generalization of it see the last Chapter of [2].

#### References

[1] | A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) |

[2] | J.E. Littlewood, "A mathematician's miscellany" , Methuen (1953) |

**How to Cite This Entry:**

Curve of pursuit.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Curve_of_pursuit&oldid=15061