# Choice, Chance and Sensible Logic

• WMDhamnekar

#### WMDhamnekar

MHB
Homework Statement
a) In how many parts, we can divide an infinite plane by n straight lines of which no two lines are parallel and no three lines are concurrent?
Relevant Equations
No relevant equations. We have to use sensible logic.
Three non-concurrent and non-parallel lines divide an infinite plane in 7 parts. and four non-concurrent and non-parallel lines divide an infinite plane into 10 parts.

Is this statement correct? If correct, we can proceed further to answer this question.

If incorrect, suggest me the appropriate rectification.

four non-concurrent and non-parallel lines divide an infinite plane into 10 parts
Or is it 11 ?

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• WMDhamnekar
So, the answer to this question is ## 1+ \frac12 \cdot n \cdot (n+1)=\frac12\cdot(n^2 + n +2)##
Now , second part of this question:
In how many parts, can we divide an infinite space by n planes of which no four planes meet in a point and no two planes are parallel?

How would you answer this question?
I am working on this question.

How would you answer this question?
Same strategy: 1 plane: 2 parts, 2 planes: 4, but then three planes: 8 parts !

• WMDhamnekar