Dave's Hypothesis is incorrect.
Basic plane geometry proofs do not allow calculated values to be used
in the proof.
For the subject under discusion, the actual value of circumference is
an innocent bystander, not a player
Once you draw a square in the circle, then you could draw both diagonals the
find the center (of course, you probably already know where the center is by
the time you've drawn a square!). Use your compass to pick up the measure
of the radius, and starting anywhere, scribe 6 consecutive arcs along the
boundary of the circle (they are the vertices of a hexagon as I described in
my previous post). Choose every other one to obtain the vertices of a
Get yourself a shashigane (Japanese Carpenter's Square) marked in the
shaku/sun system and learn to use it. Unlike American style framing
squares, they are marked on the back side for folks that work with
logs (circles). They are very handy for marking squares, and other
geometric shapes, on the end of a log, or inside a circle, without a
lot of fuss.
Dunno how a four sided figure would help, but here's a way to inscribe an
equilateral triangle using a steel square:
Use bisection to bisect the circle with a line, then bisect the 1st line at a
right angle. Draw lines from the points where the two lines intersect the
circle (4 pts). Voila! Square in circle.
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