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Topic: n dots, m lines (Read 979 times) |
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Noke Lieu
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n dots, m lines
« on: Sep 10th, 2008, 10:30pm » |
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I've been thinking about circles being cut by chords.
It's pretty famous that given n chords you dissect a circle into m=(n2+n+2)/2 regions.
My question is though, given m-1 points, such that no 3 are colinear, can the circle be dissected by n chords such that each region has no more than one point?
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Grimbal
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Re: n dots, m lines
« Reply #1 on: Sep 11th, 2008, 12:35am » |
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It seems to me that if the points are on a circle, with n chords, you cannot split the points in more than 2n groups.
For n=4, m=11, m-1=10, but you have max 8 pieces with points in it.
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| « Last Edit: Sep 11th, 2008, 12:35am by Grimbal » |
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