From: ol3@webtv.net (Oscar Lanzi III)
Subject: Re: Need hints constructing the pentagon - reply
Date: Mon, 29 Mar 1999 19:28:57 -0600 (CST)
Newsgroups: sci.math
Let me chime i with a rather unconentional approach.
Draw segment AB, construct its midpoint C and then construct the circle
with diameter AB, using C as center. Bisect AC to produce point D and
DC to produce point E, taking note of the perpendicular line at E.
Now bisect EB to obtain the midpoint F and construct a semicircle
centered on F with diameter EB. This itersects the perpendicular from E
(see above) at G. Center the compass on E and construct an arc from G
onto segment CB. The arc intersects CB at point H.
From H, construct a perpendicular to AB. This intersects teh circle at
points I and J, where both BI and BJ are sides of an inscribed regular
pentagon.
This method is closely related to the one proposed by H. W. Richmond for
the regular 17-gon, an a similar approach can be used for higher
Fermat-prime polygons.
--OL