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We consider the set E of curves with positive algebraic curvature, whoseextremities and tangents in their extremities are given. For each of the curvesof E, we define the minimum of the radius of curvature. We first prove thatthere exists a curve of E which maximizes this minimum. Numerically, we observethen that this curve is equal to the unique curve of E composed of an arc ofcircle and a line segment, where appropriate reduced to a point. This curvecorresponds also to a particular case of Dubins's curve and will be used toimprove the conception of a piece of a patent.

Existence d'une courbe \`a courbure positive maximisant le minimum du rayon de courbure -- "Observation num\'erique"