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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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 Thomas Nordhaus Posts: 433 Registered: 12/13/04
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 29, 2013 2:16 AM

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.

>
> Ken Pledger.
>

--
Thomas Nordhaus

Date Subject Author
7/25/13 William Elliot
7/26/13 quasi
7/26/13 Thomas Nordhaus
7/26/13 Thomas Nordhaus
7/28/13 Ken.Pledger@vuw.ac.nz
7/28/13 Thomas Nordhaus
7/28/13 Virgil
7/28/13 Ken.Pledger@vuw.ac.nz
7/28/13 fom
7/29/13 Thomas Nordhaus
7/29/13 Peter Percival
7/26/13 Bart Goddard
7/27/13 Thomas Nordhaus
7/29/13 Tucsondrew@me.com
9/11/13 Brian Q. Hutchings
9/13/13 Brian Q. Hutchings