Choice, Chance and Sensible Logic

[WMDhamnekar]

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.

 

[BvU]

four non-concurrent and non-parallel lines divide an infinite plane into 10 parts

Or is it 11 ?

$\$

 

[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.

 

[BvU]

How would you answer this question?

Same strategy: 1 plane: 2 parts, 2 planes: 4, but then three planes: 8 parts !