Segments in a Circle: How Many Parts Can Form & What Will It Look Like?

In summary, the maximum number of parts that can be formed in a circle with 6 segments is 22, according to the formula $\frac{c(c+1)}{2} +1$, where c is the number of cuts. This formula is derived from the pattern observed in the numbers 2, 4, 7, 11, 16, 22, ... which follows the sequence $\dfrac{n^2+n+2}{2}$. To create the maximum number of parts, all lines must be crossed without intersecting twice.
  • #1
Monoxdifly
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If a circle has 6 segments, how many maximum parts which can be formed? I know that 1 segment makes 2 parts, 2 segments make 4 parts, and 3 segments makes 7 parts. Judging by the pattern, is the answer 22? What will the exact picture of the circle be? Thank you very much.
 
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  • #2
Monoxdifly said:
If a circle has 6 segments, how many maximum parts which can be formed? I know that 1 segment makes 2 parts, 2 segments make 4 parts, and 3 segments makes 7 parts. Judging by the pattern, is the answer 22? What will the exact picture of the circle be? Thank you very much.

Looks like this sequence ...

$ 2, 4, 7, 11, 16, 22, ... , \dfrac{n^2+n+2}{2}, ...$
 
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  • #3
The maximum number of pizza pieces formula is:

$$\frac{c(c+1)}{2} +1$$

where c is the number of cuts

You'll also notice that;

the maximum number of pieces formula -1 for every number = the triangle numbers

So that's why we add a +1 at the end of the formula

Substituting c for 6 gives us:

$$\frac{42}{2}+1= 21+1=22$$

So yes, you were correct

P.S. Just so you know, you need to cross all the lines with a line to make the largest number of pieces possible, however don't cross a line intersection
 
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FAQ: Segments in a Circle: How Many Parts Can Form & What Will It Look Like?

1. How many segments can be formed in a circle?

The number of segments that can be formed in a circle is infinite. This is because a circle can be divided into an infinite number of smaller segments.

2. Are all segments in a circle of the same length?

No, the lengths of segments in a circle can vary. The length of a segment depends on the size of the circle and the angle formed by the segment.

3. Can a segment in a circle be a straight line?

Yes, a segment in a circle can be a straight line. This occurs when the segment's endpoints are on the circumference of the circle, creating a diameter.

4. What is the maximum number of segments that can intersect at a single point in a circle?

The maximum number of segments that can intersect at a single point in a circle is two. This is because a third segment would create overlapping or intersecting lines, which is not allowed in a circle.

5. How do you determine the length of a segment in a circle?

The length of a segment in a circle can be determined using the circle's circumference and the measure of the central angle formed by the segment. The length can be calculated using the formula: length = (circumference * central angle) / 360 degrees.

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