If necessary to construct the correct heptagon usually there are small difficulties. However if you do not need the ideal accuracy of the drawing and the error in 0.2% is not for you critical, you can easily make creation of such polygon by means of compasses and a usual ruler.
It is required to you
- - compasses;
- - ruler;
- - pencil.
Instruction
1. To begin construction, draw any circle and designate its center by letter O. Then carry out the radius of this circle in any direction. Designate a radius point of intersection with a circle by letter A. After that rearrange compasses in a point And yes carry out a circle or an arch of the same radius, as at an initial circle (OA). This arch will cross an initial circle in two points. Designate them by letters B and C.
2. Connect two received points. At the same time the piece of VS will cross OA radius. Designate a point of their crossing by letter D. The pieces of BD and DC formed at the same time will be equal among themselves and each of them will be approximately equal to the party of the correct heptagon which can be entered in an initial circle.
3. Measure compasses BD distance (or DC) and, since any point on a circle, lay off this distance six times. Then connect all seven points. So you receive a heptagon which with small error it is possible to call correct. All its parties and corners will be approximately equal.
4. There is also other way of creation of the correct heptagon. For a start draw any circle and carry out two mutually perpendicular diameters of this circle. Call them AV and CD. Further divide one of diameters (for example, AV) into seven equal parts. For example, if length of your diameter is 14 cm, then length of each its part will be equal to 2 cm. As a result on this diameter six marks have to appear.
5. Then rearrange compasses in one of the ends of this diameter (for example, C) also carry out an arch which radius will be equal to diameter of an initial circle (AV) from this point. After that prolong the second diameter (CD) up to crossing with the constructed arch. Designate the received point by letter E.
6. Now from a point E draw the straight lines passing only through even or only through odd divisions on diameter of AV. For example, through the second, fourth and sixth divisions. Points of intersection of these straight lines with a circle will be three of seven tops of your future polygon. Designate them by F, G and H. The point And (in case you drew straight lines through even marks) or a point In will be the fourth top (if one of straight lines passed through the next to a point And a cut-off).
7. To find the fifth, sixth and seventh tops, carry out from points F, G and H straight lines strictly perpendicular to diameter of AV. Those points in which these straight lines will cross the opposite side of a circle will be three required tops. For completion of construction you will need to connect all seven tops.