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        riddles >> medium >> Irrational Device
        
(Message started by: ThudanBlunder on Sep 27^th, 2007, 9:21pm)

Title: Irrational Device
Post by ThudanBlunder on Sep 27^th, 2007, 9:21pm

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?

Title: Re: Irrational Device
Post by Barukh on Sep 27^th, 2007, 11:40pm

:P (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1148278845)

Title: Re: Irrational Device
Post by towr on Sep 28^th, 2007, 1:18am

[hide].. 2 ..[/hide] ?

[hide]One at (0,0) for convenience, and one at, say, (e,pi)[/hide]

Title: Re: Irrational Device
Post by RandomSam on Sep 28^th, 2007, 3:12am

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...

Title: Re: Irrational Device
Post by towr on Sep 28^th, 2007, 4:42am

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.

Title: Re: Irrational Device
Post by SMQ on Sep 28^th, 2007, 5:33am

We had a similar thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1148507742) started last year with a device which removes points at non-integer distances. Can the results from there -- [hide]three points will suffice[/hide] -- be used to construct a solution for rationals?

--SMQ

Title: Re: Irrational Device
Post by Barukh on Sep 28^th, 2007, 8:51am

on 09/28/07 at 05:33:07, SMQ wrote:

We had a similar thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1148507742) started last year

Check my previous post.

Title: Re: Irrational Device
Post by SMQ on Sep 28^th, 2007, 9:04am

Who checks smilies to see if they're links?! ::)

--SMQ

Title: Re: Irrational Device
Post by FiBsTeR on Sep 28^th, 2007, 1:36pm

Why else would he post a random smiley... ??? (http://hello_world!)

Title: Re: Irrational Device
Post by rmsgrey on Sep 29^th, 2007, 6:11am

Title: Re: Irrational Device
Post by Grimbal on Sep 29^th, 2007, 3:40pm

:o (http://www.ocf.berkeley.edu/~wwu/YaBBImages/grin.gif)

Title: Re: Irrational Device
Post by ThudanBlunder on Sep 29^th, 2007, 5:11pm

What is the simplest spacing of the three devices?

Title: Re: Irrational Device
Post by Michael_Dagg on Sep 29^th, 2007, 7:12pm

An Angstrom spacing might work. That is small but
of course it depends on the resolution you require
which could be much smaller nevertheless.

Title: Re: Irrational Device
Post by ThudanBlunder on Sep 29^th, 2007, 7:54pm

on 09/29/07 at 19:12:26, Michael_Dagg wrote:

An Angstrom spacing might work.

Truly an irrational answer.

Title: Re: Irrational Device
Post by Michael_Dagg on Sep 29^th, 2007, 8:51pm

I don' think you can solve the problem with a
rational diameter.

Title: Re: Irrational Device
Post by ThudanBlunder on Sep 30^th, 2007, 8:53am

on 09/29/07 at 20:51:09, Michael_Dagg wrote:

I don' think you can solve the problem with a
rational diameter.

I had in mind 3 equally-spaced collinear devices with the square of the spacing being irrational.