Length of a circle cannot be measured precisely by a ruler, and therefore its division into equal parts is a difficult task, especially, if these parts odd quantity. Division of a circle into five parts is carried out by means of usual compasses or a protractor. Divide a circle into five parts, having entered in it the correct pentagon.
It is required to you
- Ruler without divisions, compasses, a protractor
Instruction
1. Construct a circle with the center in some point About any radius. Through the center of a circle its diameter is carried out, call it, for example AV. Construct one more diameter of this circle perpendicular to diameter of AV. For this purpose carry out from points And yes To two circles with radiuses, big than the radius of the constructed circle. Through points in the place of their crossing, and through a point About carry out diameter perpendicular to diameter of AV. Let's call it CD. By means of similar construction, carrying out a circle from points And yes Oh, construct a point E which is the midpoint of the joint-stock company. SE radius, from the center in a point E, carry out a circle and find a point of its crossing with AV piece. We will put F end to crossing.
2. The received CF piece is also the party of a pentagon which is entered in the carried-out circle. Compasses take CF piece. Let the first point of division, will be S. Provedite from it CF radius a circle before crossing with a divisible circle. From the received point carry out a circle by the same radius, before new crossing with a circle again. Repeat this operation two more times. As a result on a circle there will be five points which are tops of the correct pentagon entered in it. Arches between the received points will be equal, so, the circle is divided into five equal parts. After that it is possible to divide a circle. For this purpose from a point About carry out pieces to the points dividing a circle. As a result five sectors of the identical area which divide a circle into equal parts will turn out.
3. To divide a circle into five equal parts, use a protractor. Carry out the radius of a circle and from the center and this radius postpone a corner 36º. The corner will describe the sector which area will be equal 1/5 areas of a circle. Do this operation three more times, having received five equal sectors which will divide a circle into five equal parts.