division of space

律法

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)www.ddhw.com

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

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math59

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+1www.ddhw.com

math59

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+1www.ddhw.com