Date: Jul 29, 2013 6:23 AM
Author: Peter Percival
Subject: Re: Distance Between Lines in R^3  (fwd)

Thomas Nordhaus wrote:
> Am 29.07.2013 03:26, schrieb Ken Pledger:
>> In article <kt4635$fis$>,
>> Thomas Nordhaus <> wrote:

>>> Am 28.07.2013 23:01, schrieb Ken Pledger:
>>>> ....
>>>> That's all. It's a traditional method in old text-books which
>>>> aren't
>>>> read much any more, and it doesn't need any calculus.

>>> I think implicitly it does....

>> It needs the fact that the shortest path from a point to a line is
>> along the perpendicular. My geometry students prove that as a little
>> exercise using Euclid I.16 and 19 - definitely no calculus.

> Now, THAT is old-fashioned. What is so wrong with using calculus? That
> way you can easily generalize to minimizing distance bewtween curves,
> submanifolds, whatever. I think there is nothing "old textbook"ish about
> it. That's simply differential geometry. You will find that outlined in
> Spivak's books.

The person who posted the problem may not mind how it's solved, but
people are often interested in the most economical methods for what one
might call aesthetic reasons.

Nam Nguyen in sci.logic in the thread 'Q on incompleteness proof'
on 16/07/2013 at 02:16: "there can be such a group where informally
it's impossible to know the truth value of the abelian expression
Axy[x + y = y + x]".