How do you divide a circle into equal pieces?

Answer 1

It depends on the number of pieces that you need.

To Divide the Circle in Half:

There are two easy ways to divide a circle: using a compass or using six more circles of the exact same size.

Using Six More Identical Circles

1. Place the six identical circles around original, so that they all touch it. Every one of these circles should touch the center circle, and it's two neighbours. The fit should be perfect.

2. Mark the points where each of the surrounding circles touch the center circle.

3. Draw a line between any two opposing marks. This line exactly divides your circle.

Using a Compass

1. Set the width of the compass to equal the radius of the circle. This can be done by trial and error if necessary. That is, choosing a likely size, draw a circle, compare with original, and adjust.

2. Mark a point on the edge of the original circle.

3. Place the point of the compass on this spot.

4. There are two new points on the circle which the compass, on either side of the first point. Mark the new points.

5. For each new point, place the point of the compass there and mark one more point, as before. You should now have 5 points marked.

6. If you wish, mark a sixth point from the two newest marks. Both marks should touch the same point, if they don't your radius or your marks have been inaccurate.

7. Draw a line between any two opposing marks. This line exactly divides your circle.

To Divide the Circle in Sixths

This is the same as dividing the circle in half, above, but draw lines between all three sets of opposing marks.

To Divide the Circle in Thirds

1. Initially divide the circle into sixths.

2. These three lines should meet at the center of the circle. Mark the center.

3. Remove every other line segment between the center and the edge of the circle (circumference).

To Divide the Circle into N Equal Parts

You will need a protractor for this, and possibly a calculator.

1. Initially divide the circle into sixths, above.

2. Mark the point where the divisions cross, this is the center of the circle.

3. Remove five of the six line segments between the center and edge (circumference) of the circle.

4. Determine angle of each wedge by dividing 360 by N ( 360/N ) where N is the number of equal pieces that you want. For example if you want 9 pieces then 360/9 = 40. So you wedge angle is 40 degrees.

5. With the center of the protractor at the center of the circle and the one line at 0 degrees, mark of your wedge angle on both sides of the line. For example, if your first line is straight up and down, then mark 40 degrees to the left and to the right.

6. Draw a line from the center of the circle, through your mark, and to the edge of the circle.

7. Continue marking of your angle around the circle and drawing lines, going both directions, until your marks meet.

Further Information

There are ways to divide circles using templates that are purchased.

You may also make many more divisions using only a compass and strait edge, besides two and six, but these can be much more complex and are probably too difficult to describe without a diagram.