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

 Messages: [ Previous | Next ]
 John Conway Posts: 2,238 Registered: 12/3/04
Re: Pentagon with a sraight edge and compass
Posted: Sep 2, 1998 3:04 PM

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

Date Subject Author
8/4/98 DWill28107
8/5/98 Sarah Seastone
8/6/98 John Conway