en they come under the very eye they seem to make a
specially strong appeal. Even the person with no geometrical knowledge
whatever is induced after the inspection of such things to exclaim, "How
very pretty!" In fact, I have known more than one person led on to a
study of geometry by the fascination of cutting-out puzzles. I have,
therefore, thought it well to keep these dissection puzzles distinct
from the geometrical problems on more general lines.

DISSECTION PUZZLES.

"Take him and cut him out in little stars."

_Romeo and Juliet_, iii. 2.

Puzzles have infinite variety, but perhaps there is no class more
ancient than dissection, cutting-out, or superposition puzzles. They
were certainly known to the Chinese several thousand years before the
Christian era. And they are just as fascinating to-day as they can have
been at any period of their history. It is supposed by those who have
investigated the matter that the ancient Chinese philosophers used these
puzzles as a sort of kindergarten method of imparting the principles of
geometry. Whether this was so or not, it is certain that all good
dissection puzzles (for the nursery type of jig-saw puzzle, which merely
consists in cutting up a picture into pieces to be put together again,
is not worthy of serious consideration) are really based on geometrical
laws. This statement need not, however, frighten off the novice, for it
means little more than this, that geometry will give us the "reason
why," if we are interested in knowing it, though the solutions may often
be discovered by any intelligent person after the exercise of patience,
ingenuity, and common sagacity.

If we want to cut one plane figure into parts that by readjustment will
form another figure, the first thing is to find a way of doing it at
all, and then to discover how to do it in the fewest possible pieces.
Often a dissection problem is quite easy apart from this limitation of
pieces. At the time of the publication in the _Weekly Dispatch_, in
1902, of a method of cutting an equilateral triangle into four parts
that will form a square (see No. 26, "Canterbury Puzzles"), no
geometrician would have had any difficulty in doing what is required in
five pieces: the whole point of the discovery lay in performing the
little feat in four pieces only.

Mere approximations in the case of these problems are valueless; the
solution must be geometrically exact, or it is not a solution at all.
Fal