Convexity

In this chapter, we will define a reasonable number and verity of plane figures relating with physical object. Suppose, one of the most common physical plane figures in the plane surfaces of objects as top of oval tea table are the examples f plane physical objects. Such physical objects could be represented by the class of figures that could be cut, each in one piece, from flat sheets of paper. Some plane figures are given below.

These above plane figures have any kind of properties which associate with the physical paper figure. Observing the above plane figure. we get "all in one piece" like its corresponding paper figure, and there exist a class of set (May be set of points or set of lines) if they are not hollow. Now we denote this class of sets by S: Although the figures are "all in one piece", all are not the plane convex figure. So, defining the plane convex figure, the sets must be planar nonlinear, bounded and convex. Any physical objects has an actual shape and size and we cannot stretch away (fixed) indefinitely. This limitation to the extent of a figure is called bounded in terms of planar set before defining the plane convex figures.