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标题: division of space [打印本页]

作者: 律法 时间: 2004-11-13 08:50
标题: division of space

one plane can divide space into two parts,
two planes into four parts (at most)
three planes into eight parts (at most)
four into 15 parts (at most)

Then the question is that n planes can divide a space into
how many parts at most?

作者: math59 时间: 2004-11-13 10:51
标题: 回复：division of space

到4个平面以上就想像不出了

把他当数列做
N1=1+1
N2=1+1+2
N3=1+1+2+3
N4=1+1+2+3+4
Nn=(n-1)+(n-2)+(n-3)……+1=n(n-1)-(1+(n-1))/2*(n-1)+1=n(n-1)/2+1

作者: math59 时间: 2004-11-13 10:52
标题: 回复：division of space

到4个平面以上就想像不出了

把他当数列做
N1=1+1
N2=1+1+2
N3=1+1+2+3
N4=1+1+2+3+4
Nn=(n-1)+(n-2)+(n-3)……+1=n(n-1)-(1+(n-1))/2*(n-1)+1=n(n-1)/2+1

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