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Topic: Distance Between Lines in R^3 (fwd)
Replies: 15   Last Post: Sep 13, 2013 1:25 PM

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Peter Percival

Posts: 1,263
Registered: 10/25/10
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 29, 2013 6:23 AM
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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]".



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