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

[Monoxdifly]

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.

 

[skeeter]

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}, ...$

 

[bio]

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