Visualizing Solid Shapes-Notes

•   The numbers with negative exponents also obey the following laws:

•   Perspective is the an of representing solid objects on a flat surface to show its height, width, distance, etc.

•   3-D bodies have different views from different positions.

•   For a polyhedron,

                      F + V � E = 2

       where �F� stands for number of faces,

       �V� stands for number of vertices and

       �E� stands for number of edges.

•   The relation F + V � E = 2 is called Eater�s formula.

Plane shapes have two dimensions (measurements) like length and breadth. That is why they are called two dimensional (2-D) shapes. On the other hand, a solid object having three dimensions like length, breadth, height (or depth) is called 3-D object. Triangles, rectangles, circles, trapeziums, etc. are 2-D Figures while cuboids, cubes, cylinders, spheres, etc. are 3-D objects. A solid is bounded by one or more surface and it always occupies some space. Its surface (or face) can be a plane or a curved surface. When any two faces of a solid meet together, we get a line segment called an edge. When three more faces of a solid meet at one point, then the point is called a vertex of the solid.

Note: Perspective is an art of representing solid objects on flat surfaces to convey the impression of distance, depth, width and height, using oblique lines and shading.