Today our topic of discussion is Concepts of space, plane, line and point.
Concepts of space, plane, line and point
Concepts of space, plane, line and point
The space around us is limitless. It is occupied by different solids, small and large. By solids we mean the grains of sand, pin, pencil, paper, book, chair, table, brick, rock, house, mountain, the earth, planets and stars. The concept of geometry springs from the study of space occupied by solids and the shape, size, location and properties of the space.
A solid occupies space which is spread in three directions. This spread in three directions denotes the three dimensions (length, breadth and height) of the solid. Hence every solid is three dimensional. For example, a brick or a box has three dimensions (length, breadth and height). A sphere also has three dimensions. Although the dimensions are not distinctly visible, it can be divided distinctly into length-breadth-height.
The boundary of a solid denotes a surface, that is, every solid is bounded by one or more surfaces. For example, the six faces of a box represent six surfaces. The upper face of a sphere is also a surface. But the surfaces of a box and of a sphere are different. The first one is plane while the second one is curved.
Two-dimensional surface: A surface is two dimensional; it has only length and breadth and is said to have no thickness. Keeping the two dimension of a box unchanged, if the third dimension is gradually reduced to zero, we are left with a face or boundary of the box. In this way, we can get the idea of surface from a solid.
When two surfaces intersect, a line is formed. For example, two faces of a box meet at one side in a line. This line is a straight line. Again, if a lemon is cut by a knife, a curved line is formed on the plane of intersection of curved surface of the lemon.
Line: A line is one-dimensional; it has only length and no breadth or thickness. If the width of a face of the box is gradually receded to zero, we are left with only line of the boundary. In this way, we can get the idea of line from the idea of surface.
The intersection of two lines produces a point. That is, the place of intersection of two lines is denoted by a point. For example, the two edges of a box meet at a point. A point has no length, breadth and thickness. If the length of a line is gradually reduced to zero, at last it ends in a point. Thus, a point is considered an entity of zero dimension.
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