You can
put this solution on YOUR website!One way to start thinking about it is to play around with a fewer number of
points, say 5 equally spaced around a circle. Label the points 1-5
Starting at point 1, draw lines to the other 4 points. You have 4 lines,
or (5 - 1).
From point 2, draw lines to the other 4 points. You have 4 lines, but the
line to point 1 was already there, so subtract 1.
So far you have
from point 1: (5 - 1)
from point 2: (5 - 1) - 1
From point 3 draw lines to the other 4 points. You have 4 lines, but the
lines to point 1 and point 2 were already there, so subtract 2
Now finish for all 5 points
from point 1: (5 - 1)
from point 2: (5 - 1) - 1
from point 3: (5 - 1) - 2
from point 4: (5 - 1) - 3
from point 5: (5 - 1) - 4
Doing the additions and subtractions , I get
lines. I counted them- it works
Now I can come up with a formula for any number of points
arranged on a circle and use it for 15 points
Let
= the number of points
Let
= the number of different lines connecting the points
- (the sum 1 + 2 + 3 + 4 + . . . + (n - 1))
There is a formula for the sum. It is
which simplifies to
So far, the formula is
general formula
Now see if this formula works for 5 points
It works
Now for 15 points
answer
Hope this didn't confuse you
The general formula should work for any number of points
