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$1@news.albasani.net>,

>> Thomas Nordhaus <thnord2002@yahoo.de> 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]".