Re: Inscribing hexagon in circle

On Tue, 19 May 2009 18:07:58 -0700, David Nebenzahl
<nobody@xxxxxxxxxxxxxxx> wrote:

....
So anyone got the proof handy that a hexagon with sides of length s can
be inscribed in a circle whose radius equals s? I have my old algebra
and calculus books, but no geometry.

It's easy enough to show using Trigonometry, but that doesn't
constitute a geometric proof, which as I recall has to be done with
only compass and straight edge. But it's simple enough to demonstrate
with a compass and straight edge. I don't know whether demonstration
by construction constitutes a formal geometric proof, or not.

Set your compass to a convenient radius and draw a circle. Without
changing the compass setting strike an arc from any point on the
circle that intersects the circle. From that intersection, strike
another intersecting arc. Continue around the circle and, if done
carefully enough, the 6th arc will pass through the original point.
Since all arcs have the same radius, all the chords connecting the
intersections are the same length and equal to the radius of the arc
which is also the radius of the circle. Connect each point of
intersection with its neighbors using a straight line. By definition,
6 sides, all of the same length, constitute a regular hexagon.

Tom Veatch
Wichita, KS
USA

An armed society is a polite society.
Manners are good when one may have to back up his acts with his life.
Robert A. Heinlein
.

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