chapter  1
18 Pages

Curves

The curve is called regular of class ck if there exists its parametric representation with coordinate functionsji(t) of class ck such thatf' =J. 0. In the case of k = 1 the curve is called smooth.

Let Po be a point of "f, U-its neighborhood in induced topology. Then Po splits U into two half-neighborhoods U1 and U2• Take another point Q in one of Ui and draw the ray PoQ. If there exists the limit position of P0Q while Q tends to P in Ui then this limit ray is called the half-tangent line to 'Y with respect to Ui. If there exist two complementary half-tangent lines at Po then they form the straight line which is called the tangent line to 'Y at Po.