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Re: Two distances among Four Points

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Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:
> I don't know if Euclid knew of the puzzle.

I doubt it.  I don't remember how I learned of it some years ago.
Most probably I either invented it myself, or found it right here
in rec.puzzles!

> 
> Of the 6 solutions to the 4-point puzzle, 5 of them have very obvious geometric constructions using 
> straightedge and compass....
> but /one/ of the 6 4-point solutions does not have such an easy geometric 
> construction!
> 
> [To fully appreciate what I'm saying, I'm afraid you'll have to find the 6'th solution for yourself! 
>   Then you can try to construct it with straightedge+compass and submit your solution for extra 
> marks if you can do it! :)]

I think I constructed it 60 years ago, but I'm too lazy (and fearful of
failure!) to even attempt it with my fast-fading cerebrum.  Two comments:

(1) It was Carl Friedrich Gauss who proved that a regular n-gon could be
constructed if n's factors are all Fermat primes or 2.  This is called the
Gauss–Wantzel theorem since Pierre Wantzel proved the 'only if' part a few
decades later.

(2) A "construction" method I invented is to start with a narrow paper strip
of constant width and carefully tie a simple knot, tightening the knot
without bending the strip.  Presto!  The desired shape.

> 
> Here's my attempt at forging James' signature:
> 
> ꧁ ᩎ꧅᭾ ꧂
> 
> hmm, looks pretty close...  (I don't know what it means though)
> 
> Mike.

I've lost interest in changing my name since learning that my e-mail
server will not allow this as an account name.  The rot13 name
signed below is boring.  I read about someone who changed his name
to ZD57439 because a change-of-name was less expensive than personalized
license plate.  I'll keep looking....

Purref,
Wnzrf

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Thread

Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-17 19:14 +0000
  Re: Two distances among Four Points Charlie Roberts <croberts@gmail.com> - 2026-03-18 16:36 -0400
    Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-20 06:03 +0000
      Re: Two distances among Four Points  Charlie Roberts <croberts@gmail.com> - 2026-03-20 12:50 -0400
    Re: Two distances among Four Points Charlie Roberts <croberts@gmail.com> - 2026-03-20 11:04 -0400
      Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-20 16:22 +0000
        Re: Two distances among Four Points Phil Carmody <pc+usenet@asdf.org> - 2026-05-19 20:01 +0300
  Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-20 09:58 -0700
    Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-20 17:11 +0000
      Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-21 15:55 +0000
        Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-22 07:20 +0000
          Re: Two distances among Four Points HenHanna@NewsGrouper <user4055@newsgrouper.org.invalid> - 2026-03-23 16:16 +0000
            Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-25 02:40 +0000
              Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-25 11:44 +0000
                Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-25 09:17 -0700
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-26 07:58 +0000
                Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-26 10:26 -0700
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-27 10:25 +0000
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-27 20:27 +0000

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