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THE TWO HORSESHOES.

(Various Dissection Puzzles)
Why horseshoes should be considered "lucky" is one of those things
which no man can understand. It is a very old superstition, and John
Aubrey (1626-1700) says, "Most houses at the West End of London have a
horseshoe on the threshold." In Monmouth Street there were seventeen in
1813 and seven so late as 1855. Even Lord Nelson had one nailed to the
mast of the ship _Victory_. To-day we find it more conducive to "good
luck" to see that they are securely nailed on the feet of the horse we
are about to drive.
Nevertheless, so far as the horseshoe, like the Swastika and other
emblems that I have had occasion at times to deal with, has served to
symbolize health, prosperity, and goodwill towards men, we may well
treat it with a certain amount of respectful interest. May there not,
moreover, be some esoteric or lost mathematical mystery concealed in the
form of a horseshoe? I have been looking into this matter, and I wish to
draw my readers' attention to the very remarkable fact that the pair of
horseshoes shown in my illustration are related in a striking and
beautiful manner to the circle, which is the symbol of eternity. I
present this fact in the form of a simple problem, so that it may be
seen how subtly this relation has been concealed for ages and ages. My
readers will, I know, be pleased when they find the key to the mystery.
Cut out the two horseshoes carefully round the outline and then cut them
into four pieces, all different in shape, that will fit together and
form a perfect circle. Each shoe must be cut into two pieces and all the
part of the horse's hoof contained within the outline is to be used and
regarded as part of the area.


Answer:

The puzzle was to cut the two shoes (including the hoof contained within
the outlines) into four pieces, two pieces each, that would fit together
and form a perfect circle. It was also stipulated that all four pieces
should be different in shape. As a matter of fact, it is a puzzle based
on the principle contained in that curious Chinese symbol the Monad.
(See No. 158.)
The above diagrams give the correct solution to the problem. It will be
noticed that 1 and 2 are cut into the required four pieces, all
different in shape, that fit together and form the perfect circle shown
in Diagram 3. It will further be observed that the two pieces A and B of
one shoe and the two pieces C and D of the other form two exactly
similar halves of the circle--the Yin and the Yan of the great Monad. It
will be seen that the shape of the horseshoe is more easily determined
from the circle than the dimensions of the circle from the horseshoe,
though the latter presents no difficulty when you know that the curve of
the long side of the shoe is part of the circumference of your circle.
The difference between B and D is instructive, and the idea is useful in
all such cases where it is a condition that the pieces must be different
in shape. In forming D we simply add on a symmetrical piece, a
curvilinear square, to the piece B. Therefore, in giving either B or D a
quarter turn before placing in the new position, a precisely similar
effect must be produced.










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