# space

• Jun 5th 2014, 09:02 AM
kastamonu
space
n different spaces can divide the space into a)at most how many sub spaces?
b)at least how mant sub spaces?
• Jun 5th 2014, 09:17 AM
SlipEternal
Re: space
You did not provide enough information for an answer. The phrase "n different spaces can divide the space ..." implies that there is some space being divided. What space are you trying to divide? How are the n different spaces supposed to divide it?
• Jun 5th 2014, 10:18 AM
kastamonu
Re: space
space geometry
• Jun 5th 2014, 10:20 AM
kastamonu
Re: space
regions into which space can be divided by n planes
• Jun 5th 2014, 10:21 AM
kastamonu
Re: space
n different planes can divide the space into a)at most how many sub spaces?
b)at least how mant sub spaces?
• Jun 5th 2014, 10:33 AM
HallsofIvy
Re: space
One plane will divide 3 dimensional space into two disjoint regions but neither is a "subspace".

n parallel planes will divide 3 dimensional space into n+ 1 regions. n parallel planes and m planes perpendicular to those will divide 3 dimensional space into (n+ 1)(m+ 1) regions. If we a have total of n+ m= N planes that will b maximized by taking m and n as close to N/2 as possible. If N is even, m= n= N/2 gives $\displaystyle N^2/4+ N+ 1$. If N is odd taking one of m and n equal to (N-1)/2 and the other (N+1)/2 gives [tex]\frac{N^2+ 4N+ 3}{4}[tex].
• Jun 5th 2014, 11:29 AM
kastamonu
Re: space
according to the book n^3+5n+6/6
• Jun 5th 2014, 11:47 AM
kastamonu
Re: space