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Topic: Irrational Device (Read 863 times) |
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ThudnBlunder
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Irrational Device
« on: Sep 27th, 2007, 9:21pm » |
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A new invention centred at point O in the plane removes all points from the plane that are an irrational distance from O. What is the least number of these irrational devices required to eliminate all points of the plane?
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Barukh
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Re: Irrational Device
« Reply #1 on: Sep 27th, 2007, 11:40pm » |
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towr
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Re: Irrational Device
« Reply #2 on: Sep 28th, 2007, 1:18am » |
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.. 2 .. ?
One at (0,0) for convenience, and one at, say, (e,pi)
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RandomSam
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Re: Irrational Device
« Reply #3 on: Sep 28th, 2007, 3:12am » |
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There are 2 points on the plane that are exactly 10 units from each of those positions.
And another 2 points that are 11 units away...
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towr
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Re: Irrational Device
« Reply #4 on: Sep 28th, 2007, 4:42am » |
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Yeah, now that you mention it, there are obviously infinitely many points at arbitrary rational distances from both those points. (Always on the intersections of two circles with rational radii)
And that's true for any two points you'd start with. So at least three points are needed.
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SMQ
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Re: Irrational Device
« Reply #5 on: Sep 28th, 2007, 5:33am » |
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We had a similar thread started last year with a device which removes points at non-integer distances. Can the results from there -- three points will suffice -- be used to construct a solution for rationals?
--SMQ
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--SMQ
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Barukh
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Re: Irrational Device
« Reply #6 on: Sep 28th, 2007, 8:51am » |
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on Sep 28th, 2007, 5:33am, SMQ wrote:
Check my previous post.
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SMQ
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Re: Irrational Device
« Reply #7 on: Sep 28th, 2007, 9:04am » |
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Who checks smilies to see if they're links?! 
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FiBsTeR
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Re: Irrational Device
« Reply #8 on: Sep 28th, 2007, 1:36pm » |
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Why else would he post a random smiley... 
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rmsgrey
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Re: Irrational Device
« Reply #9 on: Sep 29th, 2007, 6:11am » |
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Grimbal
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Re: Irrational Device
« Reply #10 on: Sep 29th, 2007, 3:40pm » |
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ThudnBlunder
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Re: Irrational Device
« Reply #11 on: Sep 29th, 2007, 5:11pm » |
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What is the simplest spacing of the three devices?
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Michael Dagg
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Re: Irrational Device
« Reply #12 on: Sep 29th, 2007, 7:12pm » |
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An Angstrom spacing might work. That is small but
of course it depends on the resolution you require
which could be much smaller nevertheless.
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Regards,
Michael Dagg
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ThudnBlunder
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Re: Irrational Device
« Reply #13 on: Sep 29th, 2007, 7:54pm » |
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on Sep 29th, 2007, 7:12pm, Michael_Dagg wrote:| An Angstrom spacing might work. |
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Truly an irrational answer.
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Michael Dagg
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Re: Irrational Device
« Reply #14 on: Sep 29th, 2007, 8:51pm » |
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I don' think you can solve the problem with a
rational diameter.
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Regards,
Michael Dagg
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ThudnBlunder
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Re: Irrational Device
« Reply #15 on: Sep 30th, 2007, 8:53am » |
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on Sep 29th, 2007, 8:51pm, Michael_Dagg wrote:I don' think you can solve the problem with a
rational diameter. |
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I had in mind 3 equally-spaced collinear devices with the square of the spacing being irrational.
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