Circle Division

A circle is a closed curve. The points on the circle are equidistant from the center of the circle. A circle creates 2 regions, the interior of the circle is one region and the exterior is another region.

A circle can be divided into equal or unequal parts. The division can be accomplished by straight lines or curved lines. With every nth line the circle gets divided into n+1 parts, meaning with one line circle can be divided into 2 parts, with nth line circle can be divided into n+1 parts assuming that the lines do not intersect.

Circle Division Term in Maths:

A circle division can be accomplished by using a straight line or a curved line. As we are not considering the area calculation for this discussion, let us restrict ourselves to straight lines for the purposes of this study.

The straight line that joins a point on the circumference of the circle to another point on the circumference of the same circle is called a chord. A chord divides the circle into 2 parts.

Consider several chords on the circle and suppose some or all of the chords intersect. Then it is found that the number of area regions that the chords cut the circle into is always more than the number of chords passing through the circle.

Here is an example

The above is popularly known as the cake cutting example.

In the first picture, one chord divides the circle into 2 parts.in the second picture, two chords divide the circle into 4 parts, in the third three chords divide the circle into 3 parts and the forth diagram 4 chords divide the circle into 11 parts.

Here you see that the first cut creates 1 new region (1+1)

The second cut creates 2 new regions (2+2)

The third cut creates 3 new regions (4+3) and the 4th cut creates 4 new regions (7+4)

This is mathematically represented as

F (n) = n + f (n-1)

Conclusion for Circle Division:

Circle division is an important study in geometry that gives several clues for practical applications. There are several theorems and postulates that delve deeper into circle division and provide new insights into this area of study.