Geometry

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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 -

    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?

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