🚀 go-pugleaf

hlakota@undergrad.math.uwaterloo.ca (Hrvoje Lakota) wrote:
>
> In article <3kn6fh$1560@bubba.ucc.okstate.edu>,
> David Ullrich  <ullrich@math.okstate.edu> wrote:
> >molinari@math.lsa.umich.edu (Rory Molinari) wrote:
> >>
> >> >>>>> "James" == James Xidos <jamesx@morgan.ucs.mun.ca> writes:
> >> In article <3kkpsv$m60@coranto.ucs.mun.ca> jamesx@morgan.ucs.mun.ca (James Xidos) writes:
> >>
> >> [snip]
> >>
> >> >>>>  <tealsl@fox.nstn.ca> writes:
> >> >>>>
> >> >>>> > " A line goes through the point (2,2). It cuts the x axes at A
> >> >>>> > and the y axes at B. What is the minimum length of AB"
> >> >>>>
> >>
> >> [snipped:  discussion of why answer is zero]
> >>
> >> In this problem we can get _any_ non-negative length for AB, so
> >> zero (although possibly trivial) is not an isolated answer, and
> >> we're not going to get anything non-zero by minimizing.
> >
> >	Having made an ass of myself once already by overlooking the
> >trivial solution I feel uniquely qualified to say "Oh yeah? What line
> >gives you length(AB)=1?"
> >	The minimum is zero but it's isolated - the next-largest
> >possibility is 4*sqrt(2).
> >Dave Ullrich.
> >
>
> How about this line:
>
>   y=b/a*(x-a) where
>
>   b = 1-sqrt(5)+sqrt(-7+4*sqrt(5))/2  = approx .5791517665
>   a = 2*b/(2-b)                       = approx .8152197436
>
> This line passes through points (-a,0) and (0,b),the distance between which
> is 1, and it also passes through the point (2,2).  As far as I can see this
> satisfies all the conditions of the original problem.
>
> Hrvoje Lakota

	Remind me to think before typing in the future. (If you
think of it...)
Oh well,
Dave Ullrich