Geometry Instrument


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Solid Polyhedron

This solid polyhedron is a convex solid whose boundary is the union of a finite number of full polygons, no two of which are coplanar. The full polygons are the faces of the polyhedron; the edges of the polyhedron are the sides of the polygons and the vertices of the polyhedron are the vertices of the polygons. A segment that joins two vertices and is not in a face of the polyhedron is a diagonal of the polyhedron. A dihedral angle between two face-planes and containing two of the faces is a dihedral angle of the polyhedron. The angles of the polygons in the faces are plane angles or face angles of the polyhedron. -Regular polyhedron: A regular polyhedron is a geometric solid, all of whose faces are congruent regular polygons, in which the same number of polygons meet at each vertex or a regular polyhedron is a polyhedron whose faces are congruent regular polygons and each two of its dihedral angles are congruent. The famous Swiss mathematician Leonhard Euler, was found the there ar...
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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 ...
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