How To Divide The Circle Into 5 Parts | The Science



The Science

How to divide the circle into 5 parts

Circumferential length can not be accurately measured with a ruler, and therefore its division into equal parts is not an easy task, especially when these parts is an odd number. Divide the circle into five parts is carried out using a conventional compass or protractor. Divide the circle into five parts, inscribed in it a regular pentagon.

How to divide the circle into 5 parts

You will need:

Ruler without division, a compass, a protractor

Instruction how to divide the circle into 5 parts

Step 1:

Construct a circle centered at a point about an arbitrary radius. Through the center of the circle holding its diameter, its name, such as AB. Draw another diameter of the circle, the diameter perpendicular to AB. To do this, swipe from the points A and B are two circles with radii larger than the radius of a circle. A point at the intersection of them, and through the point O draw the diameter perpendicular to the diameter AB. Let's call it a CD. With the help of such a construct, a circle is drawn from the points A and D, construct a point E, which is the midpoint of AB. Radius CE, from the center to the point E, draw a circle and find its point of intersection with the segment AB. At the intersection point put F.

Step 2:

The resulting segment CF and a side of the pentagon, which is inscribed in a circle undertaken. Compasses take segment CF. Let the first dividing point is C. Conduct of her CF radius circle to the intersection with the circle divisible. From the resulting point again draw a circle with the same radius, to a new intersection with the circle. Repeat this step two more times. As a result, the circle will have five points, which are vertices inscribed in it a regular pentagon. Arc between points obtained will be equal, and hence, the circle is divided into five equal parts. You can then divide the circle. To do this, from the point O to draw segments, dividing the circle points. The result is a five sectors of the same area, which divide the circle into equal parts.

Step 3:

To divide the circle into five equal parts, use a protractor. Spend the radius of the circle and the center of the radius and angle of 36º aside. Angle describes the sector, an area which is equal to 1/5 of the area of ​​the circle. Repeat this operation three more times, getting five equal sectors, which will divide the circle into five equal parts.