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Topic: Req: Pentagon problem - help please !
Replies: 8   Last Post: Mar 12, 2004 7:15 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Pentagon with a sraight edge and compass
Posted: Sep 2, 1998 3:04 PM
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On 2 Sep 1998, Charlie Mead wrote:

> I would love to have this information. At one timeI knew
> how to do this, but I have forgotten.


Here's what I call the "BISECT-BISECT" construction,
which is one of the simplest. I suppose that you want
to draw your pentagon ABCDE in the circle with center O whose
Northernmost, Southernmost, Easternmost and Westernmost points are NSEW,
with one vertex being at E:


N
| A
B | |
| Y |
| | \ |
| | \|
W--Z--------O---X--------E
| | |
| | |
| | |
C | |
| D
S

What you do is BISECT the segment NO at Y, and then BISECT
the angle OYE; letting the internal bisector YX cut OE in X
and the external one YZ cout OW in Z. Then the perpendiculars
to WE through these points hit the circle in the four other
vertices A,B,C,D as shown.

John Conway





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