I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example

• 1 line divides the circle into 2.
• 2 into 4.
• 3, however into 7.
• 4 into11
• 5 into 16
• 6 into 22
• 7 into 29
• 8 into 37
• etc...

Mike Kerry(grade 12 Student)

Hi Mike

Your sequence is 2, 4, 7, 11, 16, 22, 29, 37, ... Look at the difference between consecutive terms. The reason that the pattern goes on like this is that when you draw the nth line it crosses each of the previous (n-1) lines and hence divides each of n regions into two parts. Thus drawing the nth line produces n more regions.

Cheers
Penny