Abstract
This article presents a quasidiscrete geometric model of the problem of simple pursuit on a plane by the method of parallel approximation. For each moment of time, the Apollonius circle and associated characteristic lines are constructed. In this geometric model, for the predetermined target path, the optimal path of the pursuer is found. Modeling was performed in the computer mathematics system MathCAD. Based on the simulation results, an animated video was made, where you can view the movement and transformation of the Apollonius circle and associated characteristic points and lines.
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