🚀 go-pugleaf

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