At the solution of tasks in geometry sometimes it is required to divide a straight line piece into equal parts. By the way, such task can arise also in a common everyday practice if, for example, it is required to hammer into a wall nails equally spaced. There are several ways of the solution of such task which are not demanding significant calculations.
It is required to you
- Compasses, ruler, pencil
Instruction
1. If you need to divide a piece into two or four parts, use compasses. From the ends of a piece And yes In by means of compasses carry out two arches of a circle of radius of R. Radius of a circle make a little big half of a piece of AV. Bring arches to mutual crossing. Thus you receive the points of C and D equidistanted from AV piece. Carry out through points straight lineof C and D line, AV crossing a piece. The point of intersection of this line and a piece will be a required point E in which the piece of AV is divided into two equal parts.
2. To divide a piece into four equal parts, do the procedure described above consistently with each of two turned-out equal pieces of AE and EB.
3. If you need to divide a straight line piece into any any number of equal parts 7 has to be equal. From any end of a piece of AV (for example, from a point A) draw at an acute angle to a piece a straight line of any length. On the received line from a point And by means of compasses postpone 7 equal pieces of any length, noting their ends in figures from 1 to 7. Connect the point 7 corresponding to the end of the seventh piece to a point In (the end of a piece of AV). From points 1, 2..., 6 draw the straight lines parallel to line 7B. These lines will cross AV piece, having divided it into 7 equal parts. The task is solved.