n different spaces can divide the space into a)at most how many sub spaces?

b)at least how mant sub spaces?

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- Jun 5th 2014, 09:02 AMkastamonuspace
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 AMSlipEternalRe: 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 AMkastamonuRe: space
space geometry

- Jun 5th 2014, 10:20 AMkastamonuRe: space
regions into which space can be divided by n planes

- Jun 5th 2014, 10:21 AMkastamonuRe: 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 AMHallsofIvyRe: 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 AMkastamonuRe: space
according to the book n^3+5n+6/6

- Jun 5th 2014, 11:47 AMkastamonuRe: space