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From: binder@dosadi.DEC (You are what you do when it counts.)
Newsgroups: net.math
Subject: A geometrical construction poser
Message-ID: <964@decwrl.DEC.COM>
Date: Thu, 6-Feb-86 14:46:00 EST
Article-I.D.: decwrl.964
Posted: Thu Feb  6 14:46:00 1986
Date-Received: Sun, 9-Feb-86 04:40:56 EST
Sender: daemon@decwrl.DEC.COM
Organization: Digital Equipment Corporation
Lines: 53

I've got a real poser for the geometry wizards out there.  Back in Engineering 
Drawing class, oh, some 25 years ago, I learned a technique for the construc-
tion of a regular inscribed pentagon.  The instructor, who was not a geometer,
stated that its validity was not proven and was probably unproveable.  In the 
following figure, I've faked it as best I can without a graphics tube, and
I've described the procedure.  Is there anyone who can prove that this little 
gem is valid, or that its validity is unproveable?

                                    | B
                              ____--+--____    |
                          _-''   _-/|\-_   ``-_|_-'
                       _-'    _-" / | \ "-_  _-|-_
                     .'    _-"   /  |  \   "-_ |  `.
                   .'   _-"    /    |   \     "|_   `.
                  '  _-"      /     |     \    | "-_  `
             -_  '_-"       /       |      \   |    "-_`
               "+"         /        |       \  |        +  H
             E :\"-_     /          |        \ |        /:
               |    "-_ / D         | O       \| C       | A
             --+-\-----+------------+----------+-------/-+--
               |                    |          |         |
               `  \                 |          |      /  '
                |                   |          |        |
                .  \                |          |     /  '
                 `.                 |          |      .'
                   `\               |          |    /'
                     +_-------------|----------|--_+
                   F   "-_          |        "-|-"   G
                          "-__      |      __-"|"-_
                              """"--+--""""    |
                                    |

Procedure:

1.  Bisect OA to locate C.

2.  From C, with CB as radius, strike an arc to locate D.

3.  From B, with BD as radius, strike an arc to locate E.

4.  From E, still using BD as radius, locate F.

5.  Repeat step 4, moving around circumference, to locate G and H.

6.  BEFGHB is the required regular inscribed pentagon.

Please reply by direct E-mail, as I don't subscribe to net.math.

Cheers,
Dick Binder   (The Stainless Steel Rat)

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