Sacred
Geometry exercise no. 1
Constructing
a Pentagram
 This
method was devised by 16th Century artist and geometer
Albrecht Dürer, and is by far the easiest and most
elegant method of drawing a pentagram. This is a classic
construction uniting the pentagon and hexagon, and is
accomplished in the same way as the Creator traditionally
designed the Universe, "with the opening of the
compasses unchanged". Dürer used this geometry
as the basis for several of his pictures, most notably
Melancholia (left).
Requires
only compasses and straightedge. |
 Step
1: Draw a horizontal line. This is not strictly
necessary, but it helps to keep things square to the
page.
Step 2: Set your compasses to the length
you want the base line of the pentagon to be; a-b
in this case.
Step 3: Place point of compasses at
point a and point b
in turn and draw two overlapping circles, the centre
of each on the circumference of the other. This is the
essential sacred geometric form called the Vesica Piscis.
Step 4: Bisect the vesica by drawing
a vertical line c-d connecting
the points where the two circles cross.
Step 5: Without changing the setting
of your compasses, put the point at the bottom of the
vesica where the two circles cross at point c,
and draw another complete circle. You now have three
overlapping circles, two side-by-side and one lower.
|
Step
6: With your straightedge, draw two lines e-f
and g-h diagonally upwards
from the points where the lower circle cuts the two
circles of the vesica, passing through the point where
the lower circle cuts the vertical centre line (point
o). Extend these lines until they touch
the upper edges of the two vesica circles at
f and h. These two points
will be the side 'corners' of your pentagon.
|
Step
7: Still without altering your compass setting,
place the point in turn on each of these two points
f and h
that we've just established. Draw overlapping short
arcs above and between these points to define our top
corner of the pentagon at point i. |
Step
8: Connect this last point with the previous
two and then connect those to the original base points
to make the pentagon a-b-f-i-h: |
Step
9: Finally, draw in the internal diagonals
of the pentagon to get your pentagram!
You
can erase the construction lines if you like, but it
is traditional in sacred geometry that you leave them
visible so that others can see the method of construction
and be impressed with your geometric skills. |
For
an encore, you can continue with the drawing
to produce the hexagon/hexagram. This is very easily
done; still with your compasses setting unchanged, "step
off" short arcs from points e
and g to give points j
and k. Do the same from these
points to check that you have everything accurate. This
"stepping off" technique is well-known to
most people as a method of making a six-petalled flower
shape. |
Now
draw in your hexagon a-b-g-j-k-e,
and then its a simple matter to connect the diagonals
to make the hexagram star.
Congratulations!
This little exercise has profound significance in sacred
geometry as it encapsulates the union of five and six,
life and regeneration unfolding into order and structure.
This basic form can be expanded in many interesting
ways to produce area-filling tiling patterns such as
those found is Islamic art for instance. It can also
be used to enclose three-dimensional space in the form
of a geodesic dome, which is constructed from these
basic hexagons and pentagons.
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©
Grahame Gardner 2005 |
