isocline

An isocline in a vector field f(x) is a curve along which the direction f/|f| is constant.

A particular use of the concept is to sketch solutions of ordinary first-order differential equations, ie equations of the type y'(x) = f(x, y). This is equivalent to sketching the field lines of the vector field f(x) = (1, f(x, y)). In order to do this it is helpful to first sketch the flow vectors at as many points as possible. An efficient way of doing this is to solve the equation f(x, y) = C constant for some suitable values of C (eg C = 0, ±1, ∞), ie to find the isoclines. We can then sketch the flow vectors along those curves, and hopefully see what the solutions look like from this.

Geometry

The geometric interpretation of isocline is any line indicating a constant value in a two-dimensional field. Typical examples include isobars and isotherms on a weather map, and topographic lines on a topo map.

Geology

A geologic fold, either syncline or anticline, which is so tightly folded around the fold axis that the limbs of the fold have identical strike and dip.

            ||*||            \\    *    //
            ||*||             \\   *   //
            ||*||              \\  *  //
            ||*||               \\ * //
            ||*||                \\*//
            |\*/|                 \*/
             \*/                   *
              *                    *

        Isoclinal fold       standard fold

(* = fold axis)