y = ƒ(#). On the positive side of the ^-plane take the curve lying on this cylindrical surface and satisfying the condition z = P(x) ; on the other side take the curve lying on the cylindrical surface and satisfying the condition z = — N(x). We thus intercept between two curves a part of the cylindrical surface for which x is on (ab). It is not difficult to form a fair intuitive notion of this ...

Abstract In this study, we define the generalized normal ruled surface of a curve in Euclidean 3-space E 3 . We study geometry such surfaces by calculating Gaussian and mean curvatures to determine when is flat or minimal (equivalently, helicoid). examine conditions for curves lying on be asymptotic curves, geodesics lines curvature. Finally, obtain Frenet vectors get some relations with helice...