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Topic: how many non overlapping (Read 2126 times) |
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tony123
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how many non overlapping
« on: Nov 1st, 2007, 7:37pm » |
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how many non overlapping 2 by 2 squares will fit into a circle with radies 8
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mikedagr8
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Re: how many non overlapping
« Reply #1 on: Nov 2nd, 2007, 1:56am » |
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I'll have a go at 16
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towr
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Re: how many non overlapping
« Reply #2 on: Nov 2nd, 2007, 2:32am » |
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I can fit at least 33, and that's without really trying..
[e]39 with a bit more care[/e]
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| « Last Edit: Nov 2nd, 2007, 2:40am by towr » |
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mikedagr8
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Re: how many non overlapping
« Reply #3 on: Nov 2nd, 2007, 2:35am » |
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I see why I have so few, I read 'radii' as diameter. So that's where I 've gone wrong... 
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towr
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Re: how many non overlapping
« Reply #4 on: Nov 2nd, 2007, 2:42am » |
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on Nov 2nd, 2007, 2:35am, mikedagr8 wrote:| I see why I have so few, I read 'radii' as diameter. So that's where I 've gone wrong... |
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Ah, that would make a bit of a difference, yes.
Although then you'd have a greater area in squares than your circle.. 16*22 > (8/2)2*
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mikedagr8
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Re: how many non overlapping
« Reply #5 on: Nov 2nd, 2007, 2:55am » |
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on Nov 2nd, 2007, 2:42am, towr wrote:
Ah, that would make a bit of a difference, yes.
Although then you'd have a greater area in squares than your circle.. 16*22 > (8/2)2*
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Yes, that'd be annoying. But all fixed now.
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Grimbal
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Re: how many non overlapping
« Reply #6 on: Nov 2nd, 2007, 4:10am » |
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I found a page that can fit 35 in a circle of radius 7.3 roughly. It is listing the smallest circle that fits a given number of squares up to 35.
Given the relation between number of squares and radius listed there, I would estimate the maximum number for radius 8 to about 42.
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mikedagr8
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Re: how many non overlapping
« Reply #7 on: Nov 2nd, 2007, 4:13am » |
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Are you going to write a program to prove your suspicion, or should I just be patient? 
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towr
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Re: how many non overlapping
« Reply #9 on: Nov 2nd, 2007, 5:55am » |
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I got up to 40 now.. Using parallel rows of 3,6,7,7,7,6,4
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