Re: Simple Question
- From: Jonathan Kirwan <jkirwan@xxxxxxxxxxxxxx>
- Date: Fri, 22 Sep 2006 05:56:04 GMT
On Fri, 22 Sep 2006 04:26:20 +0100, Eeyore
<rabbitsfriendsandrelations@xxxxxxxxxxxxxxxxxxxxxx> wrote:
Chris Foster wrote:
I have a simple question. This is a qustion that I was asked in a job
interview.
If there existed and infinite two dimewnsional array of 1 ohm resisters,
what is the resistance between two point seperated by a knights move (i.e.
up two, over one, or over two and up one.......etc...)
Off the top of my head I think it's sqrt(5) ohms.
I don't think so. In terms of an exact calculation, it is (2/pi) for
an "over one, up one" move. That's exact for an infinite grid as I
understand the OP's question. The "over two, up one" has slightly
higher resistance. But not so high as to be sqrt(5). That figure is
wrong on its face. At a distance of "over two, up two" the exact
answer is (8/(3*pi)), which sets an obvious upper limit. The actual
figure for the knight's move must be between (2/pi) and (8/(3*pi)) or
else between 0.6399 and 0.8488. And that is what I found when I did
it using an entirely independent numerical method, from scratch.
Jon
.
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