THE GREAT MONAD.
(
Various Dissection Puzzles)
Here is a symbol of tremendous antiquity which is worthy of notice. It
is borne on the Korean ensign and merchant flag, and has been adopted as
a trade sign by the Northern Pacific Railroad Company, though probably
few are aware that it is the Great Monad, as shown in the sketch below.
This sign is to the Chinaman what the cross is to the Christian. It is
the sign of Deity and eternity, while the two parts into which the
circle is divided are called the Yin and the Yan--the male and female
forces of nature. A writer on the subject more than three thousand years
ago is reported to have said in reference to it: "The illimitable
produces the great extreme. The great extreme produces the two
principles. The two principles produce the four quarters, and from the
four quarters we develop the quadrature of the eight diagrams of
Feuh-hi." I hope readers will not ask me to explain this, for I have not
the slightest idea what it means. Yet I am persuaded that for ages the
symbol has had occult and probably mathematical meanings for the
esoteric student.
I will introduce the Monad in its elementary form. Here are three easy
questions respecting this great symbol:--
(I.) Which has the greater area, the inner circle containing the Yin and
the Yan, or the outer ring?
(II.) Divide the Yin and the Yan into four pieces of the same size and
shape by one cut.
(III.) Divide the Yin and the Yan into four pieces of the same size, but
different shape, by one straight cut.
Answer:
The areas of circles are to each other as the squares of their
diameters. If you have a circle 2 in. in diameter and another 4 in. in
diameter, then one circle will be four times as great in area as the
other, because the square of 4 is four times as great as the square of
2. Now, if we refer to Diagram 1, we see how two equal squares may be
cut into four pieces that will form one larger square; from which it is
self-evident that any square has just half the area of the square of its
diagonal. In Diagram 2 I have introduced a square as it often occurs in
ancient drawings of the Monad; which was my reason for believing that
the symbol had mathematical meanings, since it will be found to
demonstrate the fact that the area of the outer ring or annulus is
exactly equal to the area of the inner circle. Compare Diagram 2 with
Diagram 1, and you will see that as the square of the diameter CD is
double the square of the diameter of the inner circle, or CE, therefore
the area of the larger circle is double the area of the smaller one, and
consequently the area of the annulus is exactly equal to that of the
inner circle. This answers our first question.
[Illustration: 1 2 3 4]
In Diagram 3 I show the simple solution to the second question. It is
obviously correct, and may be proved by the cutting and superposition of
parts. The dotted lines will also serve to make it evident. The third
question is solved by the cut CD in Diagram 2, but it remains to be
proved that the piece F is really one-half of the Yin or the Yan. This
we will do in Diagram 4. The circle K has one-quarter the area of the
circle containing Yin and Yan, because its diameter is just one-half the
length. Also L in Diagram 3 is, we know, one-quarter the area. It is
therefore evident that G is exactly equal to H, and therefore half G is
equal to half H. So that what F loses from L it gains from K, and F must
be half of Yin or Yan.
