From: Jonathan Kirwan
Subject: Re: Complex number quiz
References: <3D7B8D10.5070603@BOGUS.earthlink.net> <3D7CFD55.email@example.com> <6p3f9.201882$8aG1.firstname.lastname@example.org> <3D7D6CF1.email@example.com> <3D7DBD37.27C9BDEC@ipricot.com> <3D7E23CF.ABD8E3A2@nospam.com>
X-Newsreader: Forte Agent 1.92/32.572
NNTP-Posting-Date: Wed, 11 Sep 2002 04:37:27 GMT
Organization: AT&T Broadband
Date: Wed, 11 Sep 2002 04:37:27 GMT
On Tue, 10 Sep 2002 16:54:50 GMT, Fred Bloggs
>About 35.25 meters or so with a hand calculator zero-solving. There is
>nothing profound here. You add up some arc areas and one triangle area
>and you end up with an equation of the form:
>8( x^2+0.25-x*sin(theta))+ psi/2-4*x*sin(theta)=pi
>where cos(theta)=x and cos(psi)=1-2*x^2
>and x=R/D where R=length of rope and D= diameter of circle.
>Solve for x.
>I may have made mistake but this is essentially it.
Well, I can't tell about the essence since I don't follow your logic
above. But if you draw it out, you'll see that 35.25 is far enough
off to be obviously wrong, just by inspection. It's not off by just a
little difference in area. Your answer gobbles up almost 68% of the
area. Your answer does yield an angle, from the tethering point to
the two intersections where the tethered cow reaches the edge of
field's circle, which is about 90.34 degrees, though. No idea if that
means anything to you. It doesn't, to me.
I'll post the correct logic, elsewhere. But the numerical answer is
that the tether should be 28.968211826m, approximately.