Two distances among Four Points

From	James Dow Allen <user4353@newsgrouper.org.invalid>
Newsgroups	rec.puzzles
Subject	Two distances among Four Points
Date	2026-03-17 19:14 +0000
Message-ID	<1773774860-4353@newsgrouper.org> (permalink)

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Pondering the Eight Location Puzzle reminded me of a nice Geometric Gem.

How many ways are there to arrange 4 points in the plane such that
only two inter-point distances occur.  For example, one solution is the
four corners of a unit square:  Among the six point-to-point edge lengths,
four are sides with length 1 and two are diagonals with length 1.41421356.

For our purpose here, two arrangements are IDENTICAL if one can be
converted into the other via translation, rotation, reflection or resizing.

Which arrangement is hardest to think of?

Cheers,
James

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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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