Geometry

posted by Leasha Monday, September 13, 2010 at 9:04pm.

Consider the following diagram and fill in the table: It's a diagram of circles with points around the circumference based off of the table. The table reads

# of Points: 2, 3, 4, 5, 6
# of Regions: 2, 4, 8, ?, ?

For the 5 points I got 16 regions
when i use inductive reasoning there should be 32 regions for 6 points but if you draw it out there are only 30 regions. Why is this so?

• Geometry - Reiny Monday, September 13, 2010 at 9:41pm

  Even though you posted this question 4 times now, you are probably not getting any replies because, speaking for myself, I don't know what you mean by "region".
  Secondly, are we dealing with one circle? You mentioned circles, so how many.
  Or, ... is there a single circle with, let's say, 4 points on it, another with 5 etc?
  
  Looking at the # of regions the answers appear to be powers of 2
  So I would guess that
  Number(n) = 2^(n-1) , where n is the number of points on the circle.
  
  so 5 points ---> 16 regions
  6 points ---> 32 regions
  7 points ---> 64 regions, etc
  
  This seems to be a question dealing with number of subsets.
  e.g. given points A,B,C,D
  I can form 2^4 or 16 subsets
  {} -- 1
  A,B,C,D -- 4
  AB,AC,AD,BC,BD,CD --6
  ABC,ABD,ACD, BCD -- 4
  ABCD -- 1 for a total of 16
  
  Can you related this to the number of regions?