Curves couples of planar Bézier curves

The main purpose of this thesis is to investigate the parametric equations and curvatures of the curve couples of the n-th order Bézier curve in the E2 Euclidean space given that the parametric equation with non-linear control points. In this thesis, firstly, the parametric equations of the planar Bézier curve for the evolute, involute, parallel, pedal and contrapedal curve couples are obtained respectively. Then, the curvatures of each pair of curves are calculated. In addition, they have been investigated at t = 0 and t = 1. In addition choosing some special points the control points, the curve couples of the Bézier curve and the curvatures of these curve couples are examined. Finally, the results are given in detail in the relevant section.