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To
help with a personal project I needed to learn how to draw regular
polygons with only a compass and straightedge. On 2010 August
15 I started an extensive search via the internet only to find
out that there is no general or straightforward way to create
regular polygons of any number of sides. Although there are several
differing methods for creating three, four, five, six and seven
sided regular polygons and a few others, there is no apparent
process that will address the creation of any regular polygon.
Also some regular polygons are deemed impossible to draw with
only a compass and straightedge.
It is obvious that
a circle is in essence an infinitely sided regular polygon, which
therefore should lend itself to creating any regular polygon.
So I set out on a personal quest to figure out an all-encompassing,
perfect way to create any regular polygon with only a compass
and a straightedge (and of course a good surface to write on).
On the morning of
2010 August 21 I was trying yet another permutation of the many
circle and line combinations I'd been toying with over the previous
days. When suddenly I made a simple and generally perfect discovery
that, by drawing two circles double the diameter of the main circle
then placing them along the lower left portion and extending a
line through the intersection to a predetermined segment point
then on through the upper right portion of the original circle,
I could get a good measurement for the side of the target polygon.
And with every regular polygon I've tried this method I've been
able to get a fairly precise polygon. My goal was reached for
I have found an all-encompassing, perfect technique that can,
in fact, be used for every single regular polygon. Therefore I
came up with the perfect name for this technique-Perfectagøn™.
Although Perfectagøn won't replace CAD, it is perfect for
creating fairly precise regular polygons when physically drawing
with only a compass and straightedge.
PØ
An important aspect
of Perfectagøn is to use the compass and straightedge to
equally divide a line into the number of segments equaling the
number of sides that you wish your regular polygon to be. For
instance divide a line into five equal segments for creating a
pentagon. Dividing a line into equal segments can be a rather
tedious step but it is an essential aspect of Perfectagøn.
An alternative to creating a segmented line is to use graph paper
as a way to test the effectiveness of Perfectagøn. However
the specific goal is to be able to create any regular polygon
with only a compass and straightedge, therefore being able to
divide a line into equal segments is an imperative step using
Perfectagøn. The following pages present some compass and
straightedge standards that are required for using Perfectagøn
effectively, then the subsequent and necessary steps for utilizing
Perfectagøn to draw regular polygons with 3, 4, 5, 6, 7,
8, 9, and 13 sides and ultimately any regular polygon.
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